Does the Ice chest stay permently in the boat?

I used to use an ice chest for the small boat tourneys I would participate in. I would just lower a bilge pump with a hose attached over the side and fill the ice chest that way. When in use as a live well the bilge pump was put into the ice chest with the hose hooked onto a spray bar. To empty the ice checst we just pulled the hose out of the spray bar and drain it back into the lake. It worked well but my partner and I eventully biult a coustom biultin live well. We used a thru-hull live well pump for that and it did not leak. In that live well it had a drain plug at the bottom wich we would pull at the end of the day, it drained into the boat but because it had false floors nothing got wet. The coustom well also had an overflow (another hole drilled in the boat) which allowed us to run the livewell pump for long periods of time without overflowing the well.