I think I heard somewhere that that was ABBA's sign that a song was good enough. They didn't write them down, so they had to be catchy enough to remember
This has happened to me, as a person who writes music and has recorded multiple albums.
It also happened to my bandmates when we had a song we were really focusing on they would tell me how they had been dreaming about the song and having it play in their dreams.
However, I am very susceptible to earworms and it's rare for there to not be music playing in my head.
Oh it totally happens. I think part of what makes a performer is whether you find that embarrassing (like me) or if that makes you want to sing them for others.
I'm not a musician, but I like coming up with my own silly little songs. Every once in s while I come up with something less silly that I actually like and it goes through my head for a little while.
I hope my cats likes my singing, because I would never show anyone else. I've got my creative outlet already. I don't need a new form of imposter syndrome