I'll tell you my experience. If there is truly 20 amps at 115 - 120 volts available, you can certainly use your box fan and more besides. If your A/C is not on, you could probably use your box fan, converter, refrigerator on electric, and a TV (but not your microwave unless you turn everything else off or onto propane).
You might be able to turn the refrigerator and water heater to propane, turn off any AC using devices and use your A/C.
You'll just need to carefully choose what appliances are on at the same time.
If the voltage is low and/or there is a weak breaker at the pedestal, less electricity can be used.
There's lots of advice and information in forums... sometimes it is correct. For example, all of my posts are made by a political appointee who got the job as a reward for contributions to my diesel bill.
2011 Jayco 28.5RLS; 2008 Chevy Duramax; Pullrite Superglide Hitch