Well, not really.
You can run it without a battery if the alternator directly supplies power to the ignition. It may have to spin up to a certain speed before it will output enough to power the ignition, though. If it's a generator, less worries. You might want to research the type of alternator it has. Some will destroy the diodes if no battery is present. That's why I have a continous contact battery switch on by boat. When I switch from one bank to the other, it maintains contact at all times.
If you're replacing ignition systems and batteries often, have you checked the voltage regulator (if there is one)?
Geeze, Joe. Haven't you ever been so poor you only had one battery to share between two cars?
