I can confirm that it does no damage. Our second or third time camping was cold enough for heat. Our walk thru guy had told us to turn off the propane whenever we weren't using it, which I dutifully did as I packed up the RV to move from MIL to GIL's house.
Since we were on shore power at GIL's, no need for propane so I left it off. That night we discovered one of the many things missed in our walk-thru. We turned the heat on and went to sleep.
Couple hours later I wake up shivering. Durn furnace isn't cycling - so I turn it on and off. It comes right on, and I go back to sleep. Hour or so later, I wake up again shivering. @#%#@$% furnace still isn't cycling. We'll figure it out in the morning I tell myself, and switch it on and off.
After a few more times of this, I realize that the furnace is running for about 3-5 minutes, but not blowing any hot air. That's when I realize a very important piece of information - the furnace requires electric AND propane!
I got out, turn the propane on, re-turn on the furnace and voila. Worked exactly like gljurczyk described.
That woulda been nice to find out on the walk-thru - but I'll never forget it now!