Would it be beneficial to do say 100-150 push ups every day?
I wouldn't do them everyday. You realizie that, even if resricted to once a week or so, this exercise at that intensity would be poorly suited to building mass. However, depending on your fitness level, 100-150 pushups may be a great addition to your chest regime.
To state that you'll likely overtrain is a bit premature in my opinion. As far as benifit is concerned, three obvious ones come to mind. First, I've know many men that practiced the exercise regularly as part of a PT program who developed absolutely sculpted (not huge) pecs. Second, as an addition to a mass building weight training program, a set of high rep pushups can actually facilitate faster recovery by increasing blood flow and exchange in the muscle. Third, some degree of endurance work can have direct and positive effect on the level of intensity you are able to achive when pushing the big weights around.
Now, back to the issue of overtraining, I would refer back to icelandic's comment, "when in doubt about recuperation, lower the volume."
All that being said, oubeta, this inquiry belongs on the training board.