The biggest problem is the inefficiency of a typical roof mounted AC unit. Yes, it can be done, but your system will be expensive and very heavy. You will need around 1,000 lbs of available CCC and at about $5k to do it.
I will be building a boondocking rig with a solar powered super high-efficiency heat pump, capable of AC and heat. I will be using this one, the HSAC-12A/C: http://www.geinnovations.net/Specifications.html It does not need an inverter, but uses 48v DC power, so I will be building a 48v battery bank and adding about 1,500 watts of solar to provide enough power.
So while doable, there are some hurdles to overcome. Plan on spending at least $5,000 on the new heat-pump, 48v battery bank, solar panels, inverter, wiring, brackets, etc. - that is if you do the work yourself. If you don't have the available CCC and need to go with Lithium batteries then your battery bank alone may exceed this cost estimate, though your weight will be reduced by about 400 lbs - to the 6-700 lb system weight range, if using high efficiency solar panels like these http://sunelec.com/solar-panels/sun-435w-modules-grade-b.html.
Expensive? Certainly, but if you are a FT RVer the savings in RV park expenses alone could pay for your system in as little as 2-3 years. Plus you have the added convenience of being able to stay in beautiful, remote boondocking locations in relative solitude, in climate controlled comfort, as few others will be willing or able to do.
Chip