There's very little space on board a submarine. If the Navy was willing/interested in putting paper-based workflows onto Android devices, it could save a good amount of physical space on board.
I just don't see the phone-sized form factor working too well. Maybe for taking log readings or simple lineups shifts it would be nice, but anything beyond that is either going to require SUBSAFE certification (e.g. fly-by-wire interfacing) or need to be tablet-sized or larger (e.g. running DC Central or looking up operating procedures).
And God only forbid you drop one of those mobiles in the bilge...
Like the other commenter, I think the opportunity is more for tablets, too.
There are just so damn many things that need to be logged and tracked on paper and that don't have anything to do with [reactor operations, SUBSAFE, emergency/DC procedures]. If you can reduce the stacks of binders and/or manuals, and also improve process compliance, it would be well worth the effort.
Don't forget that Android is not just for mobile phones (cell phones for our friend from across the pond). Think of it as a portable personal device running an open sourced operating system with an emphasis on touch based UI.
This made me think of Halo/Star Trek, I can imagine a commander on deck speaking into a navy spec android device 'Captain's log, gregorian calendar date ...'
In all seriousness though, I forgot how premium physical space is on a submarine, this makes sense to me!