First, get a 50/30 reducer. (Avail at Wallyworld and Campworld.
Yes, your A/C will work. HOWEVER, a caution- Don't try to run it on 30 amps with the microwave or other appliances running or you will blow the breaker and may well toast your AC. I am very cautious about what we do when running the AC on 30 amps. I did toast an AC, so I don't want to repeat that experience.
The big thing is that when you initially turn your AC on, it will draw 20 amps. After starting, it draws fewer amps. I have ran my microwave with the AC running, but only after the AC cycles. Never started the AC with other appliances running but one time, and it did take out my AC. Again, caution.