No; German was my first language and that just doesn't sound right. My best guess at deciphering the grammar rules is that "kein" is an adjective and modifies nouns, while "nicht" is an adverb. In English, one might say "No audience (allowed past this point)" or "The audience is not allowed past this point." In the former, "no" modifies the noun "audience" and is an adjective; in the latter, "not" modifies the verb "is allowed" and is an adverb. To improve the parallel to the German text, imagine an audience member asking asking the stage door guard "Who is allowed past this point?" I would answer either "Not the audience" or "No audience," but not "No the audience."
I like "audience" as the best translation. A Publikum is a group of people watching something. A "crowd" can just be a group of people doing anything. We would prefer to keep as much of the meaning intact during translation. If you want to maintain the broad meaning of "crowd" with a translation into German there are other possibilities such as Menschenmenge.