Well do they, do they have pumps to get rid of a little water that creaps in?
Yes they do quite a bit actually. Mostly due to seals on the seawater pumps and also around the shaft seals. Seawater lubricates and cools some seals. The water is collected in bilges or tanks and pumped overboard.
Back in the day, we used to send newbie sailors back aft to “check on the main shaft seals.” Particularly if the sub is deep, the amount of water pouring in is rather surprising. Anyway, when the newbie reported back that water was pouring into the bilge, we’d all scream, “Oh, no! We’re all going to die!” Much hilarity then ensued. 
Another fun thing to do is to send the newbie to the broom closet, giving him false directions, only to have him open a hatch to the outside! You’d probably laugh about it for days.
Or start up a rifle range.
Submariners (even newbies) are generally trained well enough that they quickly realize that, had the situation I described above actually been serious, actions would be taken by the trained members of the crew beyond running around and mock-screaming.
Oh, hell, we used to pull crap like that all the time, like telling newbs to go get a case of frequency oil, or to go find a skyhook.
I forget why we stopped.
I would imagine they’d leak quite a bit. You know, with all those screen doors.
…or “relative bearing grease,” as well as some “shoreline” for tieing up to the pier, not to mention looking out for the “mail buoy.” 
Or a spool of pipe thread.
Send em back to feed the shaft seals?
Air Force geeks all know about getting a bucket of prop wash.
Or used to.