I had success running an older 13.5 AC unit with an EU2000i, but cycling the compressor may be a problem. You basically have be running only the AC with nothing else taking power for it to work and even then it is working the generator at 100%+ load all the time. I had to turn the fan on low first then switch the compressor on. The fan and compressor starting at the same time were too much load and would trip the generator out.
Basically, it can be done, but it is a far from ideal situation and will likely decrease the life of your generator.