Not in most cases. The chain oil is put on drive chains every 300 miles or so. You can do the same while it is being towed by the front wheel with a stop anywhere, such as a gas station every few hundred miles. The bike is in neural and has no connection to the engine. Simply spray chain oil onto the chain.
Very few motorcycles have an auto-transmission where towing on the front wheel withn the rear wheel on the ground can be a problem.
It can also be a problem on my electric motorcycles as they have no neutral. The rear wheel is always a direct connect to the motor and I would not want to try to tow them that way without removing the belt or drivechain.
The motorcycle driveshafts are spinning in gear oil, or in greese on some bikes. Makes no difference if the motorcycle has the engine running.
Also belts do not need to be touched.
FWIW, chains are a hassle on motorcycles, IMO.
I own three of the four types. Chain, belt and shaft motorcycles.
The one I do not own is the direct drive electric (The Verge Electric shown below--the rear wheel is the motor):
View attachment 2458694
-Don- Reno, NV