It's not going to catch on fire or create sparks. But it's not the worst idea either to NOT leave your PC on overnight or when you leave the house until you've had a chance to run it for a while and make sure it's NOT going to cause a problem. Nobody, NOBODY, can tell you for sure that anything is going to do one thing or another. You'll get no guarantees here, all we can say is that it's unlikely or yes, it will likely happen. There is never any without a doubt your $#!+ is going to burn up or there is NO possible chance of anything bad happening type answers to be found. There are simply too many variables to consider and the universe has a stick sense of humor so it's up to you to use common sense and a little bit of gun shy at first wouldn't hurt.
Honestly, I don't understand how people always manage to do this in the first place. Even back when I was young, with no experience, doing my first few thermal paste replacements, it was never even something that almost happened or that I had to be particularly careful of, and still isn't. Shouldn't even HAVE the tube of paste anywhere near your motherboard in the first place. Put your TIM on your CPU while it is out of and away from the motherboard, so that can't happen.