"Wet stacking" is primarily a concern with diesel engines. When the fixed speed engine is not heavily loaded, unburnt fuel wil collect in the exhaust system. When the system is subsequently loaded, this unburnt fuel will finally ignite. Now you have a chimney fire or alot of nasty soot plus flaming debris coming out of your exhaust stack.
The little generators (<20 KVA) that are gasoline or propane powered don't suffer from this problem. It still makes sense to load them electrically. Not loading them is similiar to letting the car idle all day to keep the interior warm in winter. It is not very economical and it accelerates mechanical wear, but it typically will not cause a fire.
Mechanically speaking, it does make sense to operate the engine on a monthly or quarterly basis to ensure that moisture is driven out of the oil, the fuel in the carb is replaced with fresher fuel, all of the moving parts are exercised to keep them lubricated, etc. The important thing is to get everything up to normal operating temperature. Loading the generator will cause that to hapen quicker, than letting it sit at idle or no load.