Eh, we have actual examples of that. Dolly Parton loses Dolly Patron Look-Alike Contest, Chris Reeves being able to go out unnoticed normally but not if he's in his Superman costume.

I think most people would be more able to go unnoticed in normal clothes as opposed to a Superman costume

There’s an old story about a journalist who was interviewing Marilyn Monroe, and as they were walking down the street no one recognized her. Then she said to him “Would you like me to become her?” Then she suddenly changed how she carried herself and people around were like “omg it’s Marilyn!!!”

Henry Cavill in NYC /in a Superman t-shirt/ and being ignored.