I have a trifold "hard" cover, and it leaks. Especially where it meets the tailgate. I use the soft touch setting at the car wash. I would GUESS that the soft roll up would be fine, but that's just my guess, as I said.
The inside of my truck bed is FILTHY because we haven't had rain in 6 weeks, and if you drive a short distance on a dirt road, the cover will leak the dust. I will just fold the cover up and hose the box out.
Depends on what you mean by "problem". I have a soft rolling cover and have gone through touch-less car-washes probably about a dozen times. The car wash does not damage the cover, but it does leak a little bit into the bed due to the high pressure water coming in from different angles.