Several years ago I purchased a used Honda EU2000i and like many others thought I'd see (mostly out of curiosity) whether it would successfully start & run my Coleman Mach 3+ 13,500 BTU A/C. With fresh premium grade non-ethanol gas, fresh dino oil in the crankcase, and a new plug it ran properly at full speed but did surge somewhat with ECO turned on, a situation I managed to clear up with a generous treatment of SeaFoam in the gas tank and SeaFoam sprayed directly into the carb throat. However, it would not start my A/C ... adding an SPP6 hard start cap to the A/C didn't do it, wiring up the thermostat so I could start the A/C compressor first, then manually switch the fan on once the compressor had ramped up to speed also still didn't do it. I then dumped the dino oil in favour of Mobil 1 synth ... and the A/C started right up. :B I could even then switch the ECO mode on, the genset would slow, but still be able to ramp back up to speed without collapsing on it's face as the compressor cycled on/off. The downsides? - elevation was close to sea level and it would only do it if the outside ambient temperature was 85F or below ... increase either and it became evident I'd need a larger genset. Regardless, there was also no doubt that running synth oil in the crankcase noticeably improved how this genset handled any other loads it was asked to support, including the trailer's microwave oven. I now own my second EU2000i, likewise run premium grade non-ethanol Sea Foam treated gas and Mobil 1 synth oil, and it too starts in one or two pulls even after sitting a month and will run any load I ask of it other than the Dometic A/C on our current trailer. JMO, but I'm convinced and would only ever run synth oil in any genset I may own. :)
