+1 for that. I bought one of those cheap Chinese atvs for my daughter. It was used and the starter didn't work. No recoil or kick on it so I tore it apart. Basically rebuilt the brush holders and cleaned the armature. If you've never done it, chuck the armature into a drill and use some 180 grit or so sand paper to clean it.As for your starter, I'm sure it's gummed up with gunk from the ages. replacing the brushes is a good start. clean the hell out of the armature as well. starters are relatively simple electrical motors, if everything rotates freely it should be all right.
The regulator/rectifier is a more common problem. That and no, the alternator (which includes that stator) does not provide enough electricity at idle to run the bike. At idle, it's actually running off the battery.Still should have nothing to do with battery because the stator should provide enough juice to run the bike and keep a proper idle.