Generators are as tough as a 2-dollar steak. At worst, it might have to be re-polarized. Don't worry about disconnecting anything unless it makes you feel better to do it. OEM-replacement solid state voltage regulators definitely need to be disconnected or removed, however. Alternators, or any other solid-state devices- - - -definitely disconnect or remove them! Voltage spikes created by welding can, and do damage parts with diodes, transistors, integrated circuits, etc. That's particularly true of computers, CD players, digital clocks, or anything else with a constant-voltage "keep alive" circuit.
Jerry