In general, inverter generators such as the Honda will not have a low voltage issue when they are under too high a load. They will just trip out. So, I would not worry about low voltage issues. The Honda will either run the AC unit, or trip out. However, if the inverter in the Honda is under a long term load, close to it's rating, it is my understanding that the inverter life (inside the generator) will be shortened. I am not sure about that, it is something I seem to remember reading about them. Nor do I remember any statistics about how much the life might be shortened under high load.
When running the Honda and AC unit, I would be very sure that I had good connections, and no light extension cords between the Honda and the rig. That is where you would experience the most voltage drop.