daily? probably. it will definitely effect your "push" workouts. tris, delts and chest will be constantly bombarded with 2-300 pushups daily, which can affect recovery time. like anything your body will get used to it and eventually it can be "just the daily routine" but i wouldnt recommend it, at least not daily.
instead of normal pushups buy a swiss ball and do it on that. it is so much better well manly for sports but its been giving me alot of def to. and now i just started putting weight on my back. this is how i do it. i put my feet on a chair then my hands on the ball with my fingers pointing out so my wrists dont gt hurt.