That said, there's a marked difference between the kinds of assymetrical communication that you're describing and baby sign language. We've done sign with each of our three children and it's remarkable to watch them pick it up—they clearly understand that these hand gestures are words that carry specific meaning and get a lot of delight out of learning and applying them correctly and being mimicked and understood. The language center of the brain clearly develops much faster than the parts responsible for controlling the tongue, and sign gives them a great outlet for that language.
Also, you don't have to do anything complicated to give them just a little bit of sign, so unlike a lot of parenting advice it's not difficult to try out. Just say a word while making a sign (ASL if you want but we'll sometimes just make up one on the spot) and then give them the thing or do the thing. "More", "water", "milk", "diaper", "good night", "up"—just pick one and try it! Once you start and see their delight it's hard to stop.