They run for ages. The bilge pumps won't work under a big load so you won't have massive pressure and you might find the flow drops back a bit when the voltage drops a bit. how long exactly it runs depends on the charge in the battery, the strain on the pump - they aren't designed to pump really dirty stuff or move water uphill much.
and you do need to match the size of the bilge pump to the right sized battery.
the big downside is the battery weight. you can't carry a big heavy deep cycle battery too far. thus complicating matters if you are trying to substitute a dredge for a deep cycle setup so you have something lightweight to be mobile.
and it doesn't get around the law by avoiding using an engine. a bilge pump is still technically a mechanical device i understand.