No fuel, no fire. So yes, it can. But we have no idea what type of generator you have. If 002A or 003A, you have central injection pump. Could be pump, could be injectors. If 802A, 803A you have multiple pumps and injectors. You need to isolate which injector or which pump is at fault. In addition, you need to solve your engine problems before electrical problems. Too much to diagnose at one time. If the voltage and frequency are jumping around but the engine is super-steady, then you have other electrical issues. You need to isolate the possible fuel issues. If you are running your generator without FIRST cleaning and replacing all filters and blowing out all fuel lines, you may have sucked crud into injectors/pumps.