Yes. The overhead is for the carry-on bags. If there is space after everyone has gotten on the plane, then go for it, throw the coat up there. But if you use overhead space for a coat when they announce that space is limited and you see them forcing people to check bags, then that’s a jerk move for sure.
I pack my coat in my bag. If it doesn’t fit, I wear it on the plane. If that doesn’t work, then it’s time to start thinking about checking a bag from the start.