While not technically the same thing, all 3 of my past and present Jeeps (55, 81, and 75 CJ5's) have never had tops on them aside from bikinis and never suffered any appreciable rainstorm damage. During the summer monsoons the seats tended to get a little "wet dog" smell, but once it dried out the smell went away. With the TJ I'd only be concerned with your radio and other dash mounted electronics, the seats and rug should dry out and be fine.