Not crazy. Your understanding of the Volt's setup is right.
Two DIY examples of the same basic architecture:
1997 Chevy Cavalier EV with onboard range extending generator:
Alain St-Yves' 1997 Chevrolet Cavalier
2000 Mazda Miata EV / onboard biodiesel generator
Pat Beirne's 2000 Mazda Miata
The Miata's EV Album page is outdated. The EV systems were somewhat rebuilt and the genset added to the trunk about a year ago. More info on this car:
Building the "Zero-Carbon Car" out of a Miata, incl. biodiesel hybrid drivetrain - AutoblogGreen
The only flaw in your plan is the engine size. If you deplete the battery pack and want to continue driving, you will need a generator with a
lot more power than a scooter engine - you'll essentially need an engine with, at minimum, about 1/3 to half the power of the original gas engine.