My Yamaha 2400ISHC will start/run my older model 13.5K BTU A/C unit. It started it with some strain (running was never a problem) but every now and then it would activate the generator's overload circuit.
After I installed the Supco start capacitor it starts it every time within 1 or 2 seconds so the capacitor will help. If you've already purchased the Honda 2000 you have nothing to lose by trying the generator/capacitor combination (don't over do it if it doesn't work after a few tries).
If you haven't already purchased a generator I'd recommend the Yamaha 2400ISHC over the Honda 2000. The Honda 2000 has a 1600 watt continuous output with 2000 watt surge. The Yamaha is 2000 watts continuous and 2400 watt surge.
