Assuming that you are talking about a 12 volt battery on your generator,
your truck battery jump should be just fine.

IF the battery is shorted internally, AND ONLY TESTING WILL DETERMINE THIS
!! But if it is and he goes to jump it the battery in the truck could
explode in his face!

Get the battery tested! No normal battery would destroy a charger unless
there is something seriously wrong.

Go here if you don't believe me, DC is in many ways more potentially
dangerous than AC for the DIY.

http://www.google.com/search?hl=en&q=battery+exploding