I don't believe it would charge. It may even discharge the battery, overheat the generator or worse. A 12 volt battery requires 13 or more volts to charge.
However, I have been told that our 6 volt generators can be adjusted to put out a higher voltage.
An interim step would be to use an 8 volt battery and see if the generator can be adjusted to charge that. I run an 8 volt battery in my Model T