You won't necessarily be famous, but people may ask for you. Not by name, but they may say, "Hey, where's your curator? I want to ask her a question about this painting," or "Hey, where's your curator? She's parked in my spot."
You may, however, get a job as a curator for a famous museum, and that's almost as good as being famous. If you can tell someone, "I'm the head curator for the National Gallery of Art in Washington, D.C.," you are sure to receive some nods of genuine respect. Unless you are telling someone without any culture, in which case you might as well have told them that you work in the Portable Electronics department at Best Buy.