Yes, you should be able to. But, as already said, don't run anything else when running the A/C, and be very careful about what extension cord you use, if any.
If regular RV cord won't reach the 20 amp outlet without an extension, instead of using a typical household extension cord, I'd recommend getting a 30 amp RV extension cord, and using that.
That way, you can be pretty sure that voltage drop over the cord won't be a problem, and you'll also have an extra RV extension cord you can carry with you in case you need it at a campsite later on.
