Mine can, and I have a 13.5kBTU. A lot of newer ACs have 'soft start'. Extra capacitors on the compressor motor that help the start up surge for that very reason. I would recommend you borrow a friend's 2000 and try it before you write it off.
That being said, I have had several RVs over the years, and all of them have had one thing in common - an Onan generator that was a royal PITA. Every single one of them was unreliable in some way, form, or fashion.
My latest RV has no built in gen, a 3kw inverter, a bunch of batteries charging off solar, backed up by either a honda 1000 or 2000, whichever one (or both) I decide to pack along.
