I agree with that. Bilge pumps depend on battery. Battery dead = sunk Sea-Doo. And a bilge pump will not save you when you are riding your ski if water is coming in fast. My 2003 is completely sealed after 15 years. You have a lot to look for. Have you looked under first? Fiberglass can become permeable. I had the gel coat redone on mine just because of that possibility. If fiberglass on the keel is "grained", it could be your issue as well as a few seals here and there.
Also, is it leaking when not running and in the water for several hours?
Benji.