You're better off to disconnect the battery when you're welding. What if your car has a bad ground? It becomes a liability for the welder. It's easier to disconnect the battery than to replace electrical components.
What if your car has a bad ground?”
If you had a bad ground you would never to be able to strike an ark with electric welding. Stick or MIG...
Trust me, I’m not only a EE, but a physicists and a welder. The last thing you want to do is remove the battery. The battery would act as a low impedance shunt between the positive and negative side of the electrical system in a car, making it even more vulnerable.
I don’t know if you realize this, but the average square mile in the U.S. has 25 Lightning strikes a year and the average energy released in each one is equivalent to .0071 kilo tones of TNT. Your television survives, so does your car and most of the time your computer.
Considering that electromagnetic pulses decrease in amplitude with the square of the distance, that’s significant. You don’t need to worry too much about this...