Has anybody ever sealed off the bilge compartment so water doesn't go to the little compartment towards the front of the boat in the cabin. That way any water just stays in the bilge. Is there a downside to doing what I'm thinking about doing?

Yes you will not Be able to drain the front

Drain the front what? I don't use the ice chest or the sink. I do hose down the floor though.

bad idea, water is going to ultimately in above that last fire wall either during rain, while its stored etc. You would be opening your self up to rot.