No, that would be Maiar who can choose their appearance, not Elves.
According to
The Hobbit, the Wood-Elves were feasting at a fire, and Bilbo and the Dwarves found that
Quote:
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The smell of the roast meats was... enchanting...
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Since the Elves did not welcome their unexpected guests, it is to be assumed that they planned to eat the meat themselves. The Wood-Elves also went hunting in the forest, we are told - and that word normally refers to animals, not vegetables!
The way Galion, the butler, is described, I could imagine that he would be well-rounded, since he loved drinking and feasting.
Now, we can quibble about
The Hobbit not being quite canonical for Middle-earth as it is written in LotR. We could also debate whether the other Elves in Rivendell and Lothlorien might have had other eating habits than the Wood-Elves. And of course, it is possible that the Elves in the Undying Lands had changed their menus completely. At any rate, this is all the written evidence I could find concerning the diet of Elves in Middle-earth.
Perhaps HoME has more...