Can't speak specifically to the Club situation but assuming this layover involves an overnight, I doubt the lounge is open from 12 or 1 am to 5-6 am.

The Chinese central regulation says you are entitled to 24 hours transit without visa and that you may leave the airport. This applies to CAN, but they are known to be stubborn about letting visa-less people on transit leave. However, there are enough reports of people doing just that--usually by standing firm, knowing the regulation, and demanding to be let out. Cases are helped by showing confirmed hotel reservation for the night, and your onward boarding pass or confirmed itinerary that shows conformance with the 24 hours.

If it were me, I'd feel pretty confident I could manage to get myself let out. Not sure about your confidence level. I had thought that with layovers this long and since flying premium class, China Southern would give you hotel vouchers. You might try this tack, even if you only use the vouchers to get past the transit immigration and then go to the Pullman instead. I've heard the hotels CZ uses for overnight transiters are not great but have no first hand knowledge.