Running the generators in parallel is interesting. I would be curious to know how they deal with keeping the inverters "phase synced".
Using a motor to drive an alternator, to feed 12v power to an inverter, to produce 110 A.C., that then goes into a battery
charger, to feed 12v to batteries, just sounds like it would have a lot of conversion losses. I can see this being quite impractical to charge batteries. Too bad these type of "gensets" don't have a feed straight off the alternator to charge 12V batteries.
A typical 5000btu A/C is going to need 500-600 or so watts to run, but this will vary a bit from model to model (this assumes no other loads). However, there is is brief period of time at start up where a typical unit will require 1000-1200 watts to get started. Again this varies from model to model and assumes no other load. I would say an inverter alternator like the Honda EU2000i would run a typical 5000btu A/C, as long as there was minimal additional loads (i.e. not microwaving a burrito or running a large TV when the A/C starts up).
This is based off my knowledge of electronics and my practical experience running appliances and such off a small (1250watt) generator
at my home during power outages. In other words, I really annoyed the other "campers" with my noise and the fact I had lights
and they didn't. ;-)