I can run my A/C for about 30-45 minutes on a 15 amp circuit, no extension cord. Then the breaker trips thermally. The 15-30 adapter also gets pretty warm.
So you should do better with a 20, but the extension cord, even a 30 amp cord and additional connection resistance, is going to cost you some voltage. Try it, put in a voltage meter to see what happens to voltage inside RV when A/C is running. I don't like to see it below 108, not too much of a problem for me at home because I'm close to the transformer and get 130v at the garage outlet.
Watch all of your plugin connections, and the adaptor, for heating. If you have a problem, it will most likely be a socket or plug burning up. Especially if you have cheap 15 amp lamp-grade sockets on that 20 amp circuit.