Hi crazycro,
You did not say which camper model you have ot the AC btu size. The smaller campers had an 11,000 BTU non-ducted Brisk Air AC unit. The cold air blows out of the shroud inside the camper just under the roof unit—the larger campers with rooms had ducted AC; the cold air blew out of ducts in the rooms, and then most stepped up to a 13,500 BTU unit, which draws a little more power. All that said, I have some amp draw numbers when using my older Honda EU2000i genny.
Dave's response above is dead on. The inductive kick of starting the compressor motor and the fan at startup can spike trip many generators from getting the AC started.
My older 13,500 BTU Brisk Air AC unit spiked at 37 amps at startup, so I measured it. See here:
Once it was up and going, it would drop down to 11.5 amps
Since we boondock, I tried to see if my Honda EU2000i could start the 13,500 BTU AC unit if I shut off all 120-volt AC loads. In this case, that meant shutting off the power converter, I used the battery to run the AC control system. It worked, but I was on the ragged edge, which is not sustainable. The genny was running wide open and still jerked when the compressor came in. In my case, I have to run the power converter to charge the battery bank when we run the genny as we are boondocking. The EU2000i is just not big enough to sustain this setup. When you must charge two groups of 27 batteries on boost, the power converter consumes some of the generator capacity.
Now, enter a soft start; these help tame that high spike when the compressor comes in. I also tested that on the same generator, but I also upgraded the AC unit when the old one had a freon gas leak and moved it to a 15,000 BTU commercial AC unit. The soft start is a good thing, but this is not a lasting setup with the EU2000I. Here is a video showing the startup. You can hear the AC running in the camper, and my amp probe cannot see any high 37 amp spike like the older 13,500 without the soft start could. That link will take you to my Flickr picture site, where you can click and run the video.
15K BTU AC on 2000I genny by
John Barca, on Flickr
Last summer, during the high heat dog days of summer, we were camping in Vermont, so I tried it with our EU2000i. It worked once or twice, but the soft start stopped starting the compressor. There is not enough genny to make this work. I also had to recharge my battery bank. I even tried shutting down the power converter, which did not create a sustainable situation either.
I have a few friends with the new EU2200I, and they can make a 13,500 BTU run with the Micro Air soft start. The extra 200 watts helps. However, we never discussed the power converter's draw when charging a battery bank.
If you want to run the AC in your Sunline, a soft start does help, but even if you have the 11,000 BTU size AC, which draws a little less, what about your power converter charging the batteries? You will be on the edge, and the Genny will run flat out nonstop. The power converter may put you over the edge.
So, what are the options? I have created these because I am in the same situation, just with a bigger system. I'll do one of these when the sales start; I'm still sorting out what to do.
1. If you are lucky enough to have a newer EU2000i, you can get a parallel kit to add a new EU2200I companion genny, and the two will give you 4200 watts. Honda has a chart on serial numbers where this will work if it is not too old, like mine,

. Mine is old enough I can't use this option.
2. If you can find another older EU2000I for sale used, you can parallel them together.
Going with the two smaller generators means lifting less weight at once, but they take up more room in the truck. Odds are, with 4,000 watts, your generator will be in eco mode running the AC, and you will not break your back lifting it. Being quieter in camp is something to consider. They just cost more.
3. You buy two new EU2200i genny's and parallel them, then sell your older EU2000I
4. Honda now makes an EU3200i lower weight genny; it is like 62# when full of fuel
https://powerequipment.honda.com/gen...models/eu3200i
5. You get lucky and find an older EU3000is or a new one, they weight 130 #. I have a good friend with an older EU3000I, and his purrs quietly, running his 13,500 BTU AC. He uses a shop crane or his JD loader at home to get it in and out of the truck, and he runs the power cord to the truck bed to plug it in. So, no lifting at camp.
https://powerequipment.honda.com/gen...odels/eu3000is
I'll also add this: the Hondas are good. A heads-up on some of the cheap knockoff brands and lower wattages: Then the story starts: They bought them, and they can't handle the compressor start-up spike. Research the brand and make sure someone has tried it. Can it handle the start-up spike or get a soft start.
Hope this helps,
John