Yes. If your A/C unit runs on house current (120 VAC), you don't need an inverter to test it. It's also unlikely that it will run for long through an inverter (12V DC to 120 VAC) before it runs your batteries down. A/C units typically need shore power or a 120 VAC generator.
As for testing the A/C unit, you should be able to run an extension cord directly from the external shore-power plug on your pop-up to any 120VAC outlet in your garage. As others have noted, the extension cord should be a heavy orange one, not a thin brown or white one made of zip-wire.
If the unit does not function, disconnect from shore power and check your pop-up's inside breaker box. It should be mounted near your galley, opposite the external shore-power plug. There you will find a panel with AC breakers similar to what you might see in your home. With all external power cords unplugged, you should be able to re-set any thrown breakers, and then plug everything back in and try firing up the A/C unit again.