The question in the title differs from the question in the text.
The answer to the title question is "Yes": It is certainly part of traditional cuisine some places in the world, if perhaps exceedingly rare or luxurious.
Example: The man han quan xi (or the Manchu-Han Full Course), indulged in by Qing Emperors, consisted of such treats as: Camel's Hump, Bear's Paw, Monkey Brain, Gorilla Lip, Elephant Trunk, Leopard Foetus, Rhinoceros Tail, and Deer Sinew. These are merely the Eight Treasures from the Mountain. There are also several other sets of Eight Treasures that one must assemble before one can call it the Full Course.
These other treasures consist also of a long list of other very exotic things, most of which are no longer commonly eaten by most Chinese people. With the exceptions of Bird's Nest and Shark's Fin (which are totally bizarre things to eat for non-Chinese people, but which are still very common).
This 2004 article claims that it can still be found in Guangxi.
This other 2004 article, also by TVBS, reports that a monkey was adopted by the Taoyuan County Department of Agriculture, only after members of the public saw it with its head shaven and being offered "for sale" and bought it out of sympathy and then gave it to the Department.
The Taoyuan County Department of Agriculture confirmed for the first
time that there are Taiwanese people eating monkey brains for
nourishment ... The police suspect that there are criminal parties who
are rearing monkeys for this purpose and so, besides monitoring these
activities closely, the police also wish to remind the public, that gluttony
may lead to one becoming an accomplice to the crime.
Here is another bulletin board posting with a seemingly very detailed, though uncorroborated story about a live monkey brain being served in a Guangdong restaurant.
This baidu article describes the supposed procedure used traditionally (100+ years ago):
The monkey brain serving table must be specially made. In the centre
is cut a hole, through which the monkey's head can emerge, tie up its
limbs, and tightly secure it beneath the table, have only the monkey's
head emerge, its head hair has already been shaven previously, when
eating, the owner uses a hammer to crack the skull, then use a knife
to pry open the skull, pour out the brain liquid, and the guests then
each use a silver ladle to serve themselves, and eat all of it.
This 2012 English language article tells us that "China Cracks Down On Monkey Brain And Other Wild Animal Delicacies" (though it doesn't claim that it's live monkey brains that are being cracked down upon).
The answer to the question in the text ("Is there really such a somewhat common practice?") is probably "No": Nowhere can it be called "somewhat common". (It is however of course possible that I am neglecting some undiscovered tribes in the Amazon or what-not, or some far-flung Chinese village somewhere which likes to indulge in this traditional cuisine.)