I'm trying to think what happened last time I forgot to use the shower pump while enjoying a hot shower for too long.
I think, the water level just kept on rising.
There's no direct overflow in the bilge AFAIK. Wouldn't the water level rise until it reaches the door step or the base of the locker lid below the handwash basin? Then it would overflow and find its way into the bilge eventually, through either one of these options.