As sissy Kathy says it would impact the soundboard which is kind of the point of a hollow body bass. You also are drilling holes in a fairly thin piece of wood. If you wnat to try it I would consider using double sided tape.
Are we talking electric or acoustic hollow body? If there's a magnetic pickup on the front of your hollow body, adding a thumb rest will not effect the tone enough [for most people] to notice, if at all. Many hollow body electric basses sport thumb rests and tug bars from the shop.
Sure, many times. Whether it's a hollow or solid bass, I always tell customers to stick the prospective thumb rest on with a Command Strip. That way, they can experiment with placement before any holes are drilled. Really, many players could just use the strips and forget the screws, as they have plenty of grip.