Short answer: Most certainly no, but as so often, it's impossible to prove a negative.
The Cultural Meaning of the Brain
There are many descriptions of how the brain was discarded during mummification, while other organs like the heart, lungs, liver and intestines where carefully embalmed and kept in special vessels. However, mummification processes changed over time and there are some mummies that still contain the desiccated remains of their brains, while others show that the skull was partially filled with resin or cloth.
From Variability in Brain Treatment During Mummification of Royal Egyptians Dated to the 18th–20th Dynasties: MDCT Findings Correlated With the Archaeologic Literature:
In this study, CT provided the opportunity to examine the variability in brain treatment in 12 royal Egyptian mummies from the New Kingdom (18th Dynasty to early 20th Dynasty) treasured at the Egyptian Museum in Cairo, Egypt. [...]
CT of the mummified heads of Thutmose I, Thutmose II, and Thutmose III, who dated to the early 18th Dynasty, showed intact skull bases and desiccated brains. The intact mummified brain appears on CT as a medium-density mass with an irregular undulating border that usually occupies the posterior part of the skull 2. A midline sagittal (longitudinal) fissure, which is commonly identified in mummified brains, is considered an important indicator of an intact brain 2. The CT findings of intactness of the skull and absence of intracranial embalming materials suggest that no brain treatment had been offered to the mummies of Thutmose I, II, and III.
[...]
In this study, CT examinations of the other eight royal mummies who dated later in the 18th Dynasty to the early 20th Dynasty showed evidence of transnasal craniotomy. Although it is believed that transnasal excerebration was commonly performed as part of mummification beginning in the New Kingdom (18th–20th Dynasties), it seems that the procedure covered a wider time span than has been acknowledged 2. There are examples of transnasal craniotomies dated to the Old Kingdom (4th–8th Dynasties) 14 and the Middle Kingdom (11th–12th Dynasties) [15, 16]. Although mummification practice is often said to have declined in the Ptolemaic and Roman periods, many examples of transnasal craniotomy have been documented during those periods [5, 13].
To put those mummies in a timeframe: the 18th - 20th dynasties lasted 1549 - 1077 BC, at least 400 years after the first mention of the brain (see below).
If the brain was actually the origin of the Wadjet symbol, one would expect Acient Egyptians to embalm it with great care to preserve it for the afterlife, not throw it away and replace it with resins.
Medical Understanding of the Brain
The oldest written description of the human brain is in the Edwin Smith surgical papyrus. It contains a number of medical case studies, each with a description of findings (examination), a diagnosis and the treatment (not given in some cases that were deemed untreatable).
The date of the original compilation can be assessed approximately from clues in the vocabulary and grammar as about 2,500 to 1,900 Be.
(Source: The Edwin Smith Surgical Papyrus: An analysis of the first case reports of spinal cord injuries)
The reason why this particular papyrus is of such interest is that the author was very rational and clearly followed a scientific method.
In each of these cases, the surgeon first makes his examination of the patient and determines the character of injury. The method of examination is valid, rational, and modern. The ancient surgeon elicited information by questioning the patient, directing him or her to attempt certain movement or postures, or by the surgeon's own observations, ocular (inspection), olfactory, or tactile (palpation with fingers, or manipulation with hand).
(Source: Edwin Smith surgical papyrus: The oldest known surgical treatise)
Another reason is that this is the oldest written text in which the human brain is mentioned.
For the first time in recorded human speech, our treatise contains the word " brain," which is unknown in any other language in this age, or in any other treatise of the Third Millennium Bs. c. The earliest discussions of the brain have hitherto been found in Greek medical documents probably over two thousand years later than our Egyptian treatise, which describes the external appearance of the brain as like the corrugations arising in metallic slag - an apt description of the convolutions of the brain. In a case of compound comminuted fracture of the skull, he discusses the rupture of the sack containing the brain, an obvious reference to the meningeal membranes. The seat of consciousness and intelligence was from the earliest times regarded by the Egyptians as both the heart and the bowels or abdomen. Our surgeon, however, has observed the fact that injuries to the brain affect other parts of the body, especially in his experience the lower limbs.
(Source: THE EDWIN SMITHSURGICAL PAPYRUS PUBLISHED IN FACSIMILE AND HIERO-GLYPHIC TRANSLITERATION WITH TRANS-LATION AND COMMENTARY IN TWO VOLUMES, emphasis mine)
The original (hieroglyphic) text and translation of Case 6 starts at page 186.
Shouldst though examinest a man with a gaping wound in his head, penetrating to the bone, smashing his skull [and] rending open the brain of his skull, though shouldst palpate his wound. Shouldst though find that smash which is in his skull [like] those corrugations which form in molten copper, (and) something therein throbbing (and) fluttering under thy fingers, like the weak place of an infant's crown before it becomes whole - when it has happened there is no throbbing (and) fluttering under thy fingers until the brain of his (the patient's) skull is rent open - (and) he discharges blood from both his nostrils, (and) he suffers with stiffness in his neck, (conclusion in diagnosis).
The commentry contains a section about the translation of the word "brain":
[Hieroglyphs], " brain," is a word of extraordinary interest, being the earliest refer-ence to the brain anywhere in human records. In the known documents of ancient Egypt it occurs only eight times, seven of which are in Pap. Smith. The eighth case is in Pap. Ebers (65, 18-14), which commends " the 'y4 of many whr-fish" as a recipe for preventing gray hair, when rubbed on the head. [...] This sole occurrence of the word 'y,4 in Pap. Ebers did not, however, suggest to anyone that the word meant " brain " [...]. Indeed it may designate organic substances of a viscous or semifluid consistency like marrow; for in five out of the seven occurrences of the word in Pap.Smith it is followed by the phrase "of his skull," as if to render the word 'y4 more specific. " Marrow of the skull" would thus be the earliest designation of brain.
The Look of a Real Brain
The following content obviously contains images of real human brains. Proceed at your own discretion.
Here is a video of someone preparing pork brains to eat. It's easily conceivable that Ancient Egyptians would have eaten brains as well. Try finding anything resembling the Wadjet eye in that squishy mass...
Another video of someone explaining brain anatomy. At 2:00 minutes he points to the thalamus, which looks much less exciting than in the image in the question, because it was not artificially highlighted...
Please keep in mind that this brain was fixed in formaline and is much firmer than a fresh brain. A fresh, unfixed brain is so squishy that is deforms slightly under it's own wheight. So whether or not the anatomical structures of a real brain aligning perfectly with the lines of the Wadjet eye depends on how you hold it and where you squeze it.
This image shows a disection of a fresh human brain, as the Ancient Egyptians would have seen it if they opened the skull of a human. There is no Wadjet eye visible.
Proceed at your own discretion.
The only place where something resempling a Wadjet eye is very obvious is a model of the human brain where the thalamus is highlighted in artificial colors.
Origin of the Wadjet (Eye of Horus)
The Wadjet is linked to one of the oldest myths of Ancient Egypt: The fight between Horus and Seth, in which Seth gouged out Horus's left eye.
It is supposed to be the eye of Horus in his falcon form. Many falcons in Egypt, especially Lanner falcons, have black markings around their eyes:
(Image source)
It's hard to tell when the legend became cult and the first depictions and amulets of Wadjets were created, but there are objects dated ca. 2150–1950 B.C.. At the same time, the most elaborate description of the brain (Edwin Smith surgical papyrus) is limited to it's outer appearance ("corrugations which form in molten copper") and function for the movement of the lower limbs and ability to speak.
The following image shows the Egyptian Eye of Horus (or Eye of Ra) and how how it precisely matches exact formation of the thalamus within the human brain (click for a larger image).
