It really depends on the DM.
I think a high level adventurer could be mean just about anything - pop culture is full of heroes who choose to live anonymous, quiet lives. Just because someone is Level 20 on their character class sheet doesn't mean they are a big deal in that world.
Season 3 Buffy is the Slayer who has saved the world multiple times, but to most people she's just a nobody from a small town who still gets detention and in trouble with her mom. In season 6 one story arc involves her job at a fast food restaurant.