Will a 850w generator run??

You may have been unlucky, or let it run out of fuel.
I know of several quite successfully running 'smart' battery chargers.

As a general camp generator, I have nothing but the highest regard for a GMC 850. Bought one five years ago (on special) to supply lighting for our bush camp shown in my profile, and a second as backup as I was dubious about buying a generator for $89.00 at home hardware. Let me tell you after many hours work, I cannot kill it with an axe. I share my chainsaw fuel with it, and a full tank runs it for about 14 hrs. I only run lights and a T.V. A bit smokey and with a 30m lead reasonably quite.It suffers heavy power surges on switching on more lights, and seems heavily governed by the auto governor, rather than smoothly regulated for delicate appliances, so for a general camp generator, I have nothing but praise for it. I run the lighting for three vans equating to about 9 X 60 watt globes, and the TV, and we leave one outside light light on all night. Probably best to go with one of those Honda EU models, which apparently support what you want, but cost much moreCheers....Fred.