I am always wearing my curlers out in public... to do errands, meet friends, whatever it may be. I don't find it the least bit embarressing... I mean people don't know why I am setting my hair, I could be getting marries, doing a shoot, going out that night. It doesn't matter to me what people think.
The only concern I would have for you would be ruining the curls from the heat and sweat on your head.