I would think so -- if you get permission from the school officials first! Otherwise, stay outside the fence. Usually, a good spot is where the busses drop off kids, or where the parents drop them off also is good. And this is often right near the sidewalk, which is part of the public right-of-way. But don't actually enter the school grounds without persmission.
Maybe it would help to enter a "standard contract" situation, where you give a percentage of your find back to the school, perhaps to their textbook fund?
I would ask myself what is the best you could find on a school play ground? Unless it is an old historic school what could you find at best? Lunch money?