Molyneux's Problem was published in Locke's An Essay Concerning Human Understanding in 1690.
It was a thought experiment which essentially asked whether a person who was born blind, and could feel the difference between shapes and sizes, would be able to recognise them by sight if they were made to see.
Locke and Molyneux thought the answer was no.
In the intervening 300 years, has there been any empirical evidence to support their belief?
The statement is correct: they would have difficulty making out shapes.
David Hubel and Torsten Wiesel did a series of experiments in the sixties in which they showed that there is a critical period shortly after birth during which the brain needs input from the eye in order to become organized in such a manner that a person can see. They got the Nobel Prize for Physiology or Medicine for this in 1981.
From the Nobel Prize website:
Hubel and Wiesel in their investigations were also able to show that the ability of the cortical cells to interpret the code of the impulse message from the retina develops early during a period directly after birth. A prerequisite for this development to take place is that the eye is subjected to visual experiences. If during this period one eye is sutured even for a few days, this can result in permanently impaired vision because the capacity of the brain to interpret the picture has not developed normally.
A more detailed description of these experiments can be found here
As to what kind of sensations a previously blind person would have, if their eyes suddenly began to work, I don't know. The cells that Hubel and Wiesel describe, encode information about orientation. Perhaps it is true that seeing color would be possible.
...a person who...and at the end of the paragraph we find...if they were made to see. My English skills aren't that awesome to correct it, so I tell you instead