If you are talking about the old coleman fuel ones, I'm going to say no, probably not. I guess you could always sleep with a carbon monoxide detector and hope it wakes you up, but that's a pretty risky chance to take in a tent.
There are catalytic propane heaters made for use inside a tent. Mr. Heater makes one with low oxygen shut off and tip over shut off. They still are recommended to be used while you sleep.