It depends. Some can do it and some can't. The key is voltage and how "stable" it is.
You never want the voltage at the AC unit to be under 105 volts as it can cause damage. If using an extension cord, use at least #12 and preferably #10 and keep it as short as possible. Keep the plug blades clean and don't plug in with the power on otherwise the blades will get pitted, attract dirt and not have a good connection leading to heat and damage to the plug and receptacle.
AC units are an exception to motorized equip. in that they draw more current as the voltage goes down and the breaker can trip when the voltage *seems* okay. They draw around 5-6 times running current when starting and can result in a high voltage drop initially (split second only). A hard start capacitor can help in some cases.
Depending on how far the recept. you plug into is from your panel and how far the panel is from the transformer on the street, you can have some voltage drop (under load) before you get out to the AC unit.
I would measure the voltage at the recept. in the house and also at the TT (with AC on). Don't run other items when the AC is on. A hardwired or plug-in voltmeter in an RV is always a good idea for camping and at home.