So the way an ATC will "deny" you service is by simply replying "Stand By".
Or, of course, you could be specifically told, "[Callsign], remain clear of the Class [C/D] airspace."
To answer your other question, yes, from the event briefing, you could be told to remain clear of airspace. Generally, transitions through an airspace are done workload permitting. Although I wouldn't expect you to be told to remain clear, it is certainly possible.