The damp, at least short term, won't probably do a lot of harm to the room - just any furniture & other contents perhaps. Depends also if you have an oldish house with any damp walls or single glazing etc.
On frost setting, therm valves turn on at about 8 degrees I think. This means they should only come on when weather is fairly cold. How much energy the rads would use, I havent a clue, but has to be a fraction of heating those rooms fully. Note that the rooms will need a lot of energy to fully heat them back up later if it is a traditional home with solid walls & perhaps not to modern insulation, as the structure (walls, floors & everything) will absorb the heat before the room temperature comes back. Upstairs rads in a house are not as important as heat rises, but this will rob from rest of home to some extent. If no freeze risk, & no damp issues, then turn rads off.