When under anesthesia it could be possible to blab secrets that you don't want to let out.
But if you do blab the secrets the doctors and dentists have heard it all before and will just shrug it off so there's no need to worry if it's just doctors or nurses or dentists in the room.
You're certainly not the only one who's let out secrets and said funny stuff.
Mostly though people on anesthesia will just say random funny things about the world and may say they see things such as a Unicorn or something else.