thorgal,
IMHO, you should press the issue with the dealer, just for good measure. Just be advised that typical warranty on dealer repair is 12 mo/ 12,000 miles or end of factory warranty period which ever comes first.
I'm not sure disconnecting the battery would hurt anything, but leaving it connected is a risk I wouldn't want to take.
If your carpet is that badly soaked, it may need to be replaced depending on how long it's been like that. Mildew and mold is very hard to clean and disinfect, not too mention the horrible smell it leaves behind.
There are really only a couple of places the truck will leak inside. The sunroof drains up front, the ones in the rear or the air conditioner drains, although I doubt the a.c is putting out that much water, my guess is your sunroof drains are either clogged, disconnected or pinched off (like mine were). My dealer tried to tell me that my cowl was leaking so I humored them by letting them seal it. I got the truck back the next day. It sat over night in a rain storm and was soaked by morning. So I dropped the headliner and did all the trouble shooting myself to discover that the rear sunroof drains had been pinched off due to ****-poor installation.
After fixing the problems and letting the carpet dry I've not had the problem since (fingers crossed).
Good luck!