A UPS won’t make a difference unless it’s a very high-end commercial grade UPS. All consumer grade UPS systems simply shunt the input power straight through to the output when they are not on battery. It is a popular misconception that a UPS “conditions” the power. They provide some surge protection, but unless it’s what is known as a double-conversion UPS, then when not on battery, the power coming out of them is exactly the same as the power going in.
That said I will out on a limb and say that I find the notion that a non-inverter generator is unsuitable to run electronics to be more of a marketing gambit by the companies selling inverter generators than anything else.
My hunting property does not have utilities, so we run our hunting cabins off generators. Some of us have the fancy Honda inverter generators and some have cheap Chinese generators like this one. We all routinely run device chargers, AC units with electronic controls, etc off the cheap generators. I have both types of generators. My cabin has a flat screen TV, DVD player, AC unit, device chargers, a stereo, and a microwave. All run fine (in various combinations) off either generator.
It’s fair to say that these old-school generators have poorer power quality and less protection than the higher quality inverter generators, but I’m not sure that you’d find any electronics to be picky enough to care.