semantically, yeah it could be close enough to be understood. but if I were in charge of this course, I wouldn't accept your answer as correct. I think you might confuse a few things that lead you to that translation.
- I know, VNmese words tend to assume dual roles (noun/adj, adj/adv, noun/verb, verb/adj), if not triple or quadruple ones. "nổi tiếng" does not, it can be used as an adjective only. the translation of fame would have been "tiếng tăm" or "danh tiếng".
- depending on context, "có" can mean to have, to possess. however, it can also be its homonym used along with "không" to form yes/no questions. this is precisely how "có" is used here, to ask if the listener is famous or not. the typical answer to a "có [...] không" question is either "có" (yes) or "không" (no).