Yes your generator will run the 13.5K A/C. I have twin Hondas (close to a true 30A output) run in parallel for my 15K A/C and it runs perfect. One day just for grins and giggles however, I wanted to try my small Powermate genny in the driveway. It like yours only produces 20A. So, I plugged in the trailer and ran the A/C without any problems. I will say though like others mentioned, I did NOT have anything else turned on while the A/C was running.
Also, I added a "hard start" capacitor to my A/C a few years ago, so I don't know if that was the sole reason why the A/C started right up and the 4000W genny didn't bog down.