I have done this numerous times, the only draw back was the first time when I had it set too high and woke up in a bath of sweat, damn effecient heaters in February./forums/images/icons/smile.gif
What is it that scares you, if the fuel stops or the burner goes out the unit will shut down, as it will when your batteries tire.
I would not worry about it, these are very safe robust little units, it's not like gas, it is warm fresh air, all combusted and bad gases go out the exhaust.