Yes, pretty much sure folks are using synthetic in their gensets. I use what the mfg. calls for (usually dino) because I tend to change oil in my equipment with more frequency than most and don't want to drain money away. I think, more importantly, is that a guy keep correct oil levels, especially when operating for long lengths of time.
About a week after a big storm pulls through my area and knocks out power for thousands, the Home Depot near me has a collection of nearly new generators with seized engines. Home owners run them for days without checking oil and they can't endure the abuse.