The one miilion dollar question! I know I'll probably get 20 different opinions, but I'll ask anyway. Can batteries be charged off of a generator? What is the official company position?
If a generator "surged" anywhere near the point where it would hurt a connected device, there is something terribly wrong with the generator. Bear in mind that "normal" utility-supplied power varies from 105 to 120 V (RMS), with no effect on connected devices (which are designed for that variability).