I can't understand the exact case you are referring to (and I suppose that by "pulling" you mean "polling"), but, as a general answer:
there are no cases in which the .NET Client Library switches a session between polling and streaming.
Only in the Stream-sense phase, a session opened in streaming may be replaced by a session opened in polling, but the application is not even aware of the former, temporary, session: it is only visible in the Server log.