I keep a battery charger/maintainer on my 6 volt battery in the 26. I periodically run the engine while it is in storage. The stock generator has the F.P. voltage regulator on it.
Is there any risk to any part of the system to leave the charger hooked up while the engine is started and running for several minutes?
Unless the charger is a well self-protected one, DO NOT use the starter with the charger attached. The current draw can blow the voltage rectifier in an instant. Some old selenium rectifiers MAY be able to survive. Best not to test the lights also. The ignition itself should not hurt the charger. However, some small trickle chargers may not be able to handle even that.
Basically, a 2 amp charger can handle 2 amps. A 6 amp charger can handle 6 amps, etc.