I've been re-thinking about this some and I don't see the difference between screws penetrating the boat bottom into the keel and the keel bolts penetrating the boat bottom into the bilge. Except that the keel bolts are larger.
Keel bolts are set into the keel, slathered with a sealant and the hull is lowered onto the keel. This forms an effective seal between the keelboats, the keel, and hull. Drilling down through the keel sump and into the keel violates that seal. Even if caulked, it is caulked on the wrong side, any water pressure will push the caulk away from the inside of the bilge in contrast to the caulk between the keel and hull where water pressure pushes the caulk against the hull.
A very short screw will probably not be an issue, however a larger longer screw that penetrates the hull could be. But why put a screw there at all? It is easy enough to use some adhesive caulk to secure the bilge pump to the hull. There isn't much stress on the pump, so the adhesive does not need to be all that strong. Something like 3M 4000 would work just fine and would not be too difficult to remove.