Anything with a gas engine I think will sit for over a month I add stabil, run it to get the stabil through all the lines, then shut off the fuel valve and let the motor run until the carb empties. Then I drain the fuel out of the fuel tank and use it in another engine.
Usually for restart, I just add gas and go. Sometimes gunk might clog things up, if I am lucky just running it will clean it out, otherwise I have to take things apart and spray everything in and out with carb cleaner.
Our house generator (9,000w), I usually start and run it for 20 or so minutes every fall and spring, and/or right before a big storm. It has run fine, and generated electricity just fine, for years. I drain the carb and the fuel tank after running it with stabil before I tuck it back into the shed for long term storage.
Another generator I have is a 4,000w B&S "contractor" type generator that I got for free from a customer who had bought it for Hurricane Gloria (1985), ran it for a day or so, and then put it in his basement after draining the gas. I got it a year before Hurricane Irene, which happened in 2011. After sitting for 26 years untouched, I changed the oil and that generator powered my frig, freezer, water pump, and lights for 7 days without a hiccup. So I really don't know about this "exercising" of generators so the electrical parts keep working - I had no issues for an entire week.
But definitely be aware of old gas!