Greg, I doubt you will do harm to the generator. In fact if you leave it hooked up the power generated will just go to the battery, just not enough to help the battery, naturally. Your other concern would be if your other components such as the coil, lights, etc are 6v they need to be disconnected to prevent burning them up.
I'm like the rest, I don't know what your aim is. If it is to get better starts, then definitely start with a good tune up.
It is common sense to take a method and try it. If it fails, admit it frankly and try another. But above all, try something.
- Franklin D. Roosevelt -