Yes, and there's been a lot of work with African Greys already. Irene Pepperberg and her lab have done most of the really pioneering work. They've shown that Greys can recognize colors, small numbers and in some cases produce very large vocabs. There's also evidence that Grey's sometimes overcorrect. That is, they apply complete grammatical rules to conjugate/decline words even when the words are irregular. This happens with human children as well. Thus for example, human children will frequently say "runned" when they mean "ran" or "mouses" when they mean "mice" and many similar examples. This is strong evidence that they are internalizing general rules rather than simply repeating words they've heard. Since Greys do the same thing, we can conclude that parrots aren't just parroting.