All the time. I always seem to have a tune looping around in my head. Years and years ago I was at a banking drivethru and I was I though unheard singing a little ditty by the Beatles. Dirty Maggy Mae. Over and over to myself I thought. I looked up to see all the goils in the drivethru cracking up laughing. I motioned a little bow or nod to them and completed my transaction.
Yeah, I'm always doing it. Can't help it.
I've experienced something similar. Like when I'm too focused, I'd sing mindlessly and wouldn't even notice it. It can get awkward for me when people are around, and I wouldn't really like that.