No, but burning oil will give you bad spark plugs.
BuRN
To much resistance in the spark plug wires. Start fresh with a new distributor cap, rotor and spark plug wires. Also be sure you have the correct spark plugs installed.
Fouling spark plugs can happen when the tip temperature is insufficient to burn off carbon, fuel, oil or other deposits and causes spark to leach to metal shell...no spark across plug gap will cause a misfire. Wet-fouled spark plugs must be changed as they won't fire. Dry-fouled spark plugs can sometimes be successfully cleaned by bringing the engine up to the operating temp.
That would be very rare.
No spark.
An engine that burns oil will usually foul the spark plugs. That, in turn will cause ignition misfire, higher emissions and likely damage the catalytic converter.
If the motor is healthy, the oil will burn off in a moment or two.
Diesel generators tend burn less than half the fuel that gas generators do to do the same amount of work and outlast gas engines. They also do not have spark plugs to replace or carburetors to rebuild and service.
Spark plugs don't really burn out, they foul out. A spark plug is used to ignite the fuel/air mixture squirted into the cylinder by the fuel injector. The plug sends a spark and boom small explosion. However gasoline is not 100% clean, so it leaves carbon deposits on the plug. Over time these deposits foul the plug.
The two plugs provide a more efficient and complete burn of the fuel.
AC Delco factory platinum spark plugs. GM uses very high-voltage ignition system that burn out other non-OEM brand spark plugs in very short order.