my Brooks can get slightly wet from sweating, but all in all, I figure it airs out when riding, and I do feel a diff in being less sweaty in my nether regions compared to regular seats Ive used in the past. It seems this is a factor in hardly any sore nether regions since Ive had Brooks seats (well, since I figured out how to position them properly)
I too always carry a rain cover, but have never been concerned with sweat making the leather too wet (again though, Im a light guy)