No it's not normal. For safety sake bilge pumps are normally wired so they'll function even with the batteries turned off. Sounds like someone wired it to the switched rather than the hot side of the switch. I'd move the lead to the hot side and test it to be sure it's functional.
I had a similar issue with my 2008 B43. The bilge pump was wired with the radio and also needed the main breaker turned on. Crazy, rewired and all was well.
I also have an 08 B40 and it operates that same way. I just checked the bilge area yesterday and after setting from early November what little water that was in the bilge that was a result of cleaning has evaporated. Other than when I clean the bilge I don't think it has ever ran, even after a 30 hr. rough crossing of the Gulf of Mexico.
Mike and Wayne are correct it should not be wired as the factory has wired it.
Thanks for the replies guys. Well I got to thinking that if it was wired "correctly", the batteries would eventually go dead if a detrimental leak occurred and the boat would sink in the slip.
On the other hand, if I kept shore power applied with battery charger on, at least the pump may be running when I visit the boat next and wouldn't be sunk. Guess we never know which way to go sometimes.
William, you on the gulf?
Wayne, you always want the bilge pump to work even if the batteries are switched in the off position. Replacing a burned out bilge pump is much cheaper than replacing your boat.