I took a welding course at BOCES, from a very experienced, WWII veteran. This was in the early 1990's, i.e, not nearly so much computers on board then.
And Rule #1 for Welding on a Motor Vehicle was:
DISCONNECT THE BATTERY.
He told stories of alternators (or maybe generators, on older cars? I can't remember) starting to RUN, as MOTORS, as just one example of what could go wrong, in addition to the LIKELIHOOD of exploding batteries, fried harnesses, etc....
I would NEVER leave the battery connected, while welding, under any theory (because even if the stated theory of the poster in favor of leaving the battery connected is true, you still have all the KNOWN and [more] LIKELY OUTCOMES, of the risks involved). The battery's got enough hydrogen gas in it, to throw the sulphuric acid it contains, far and wide, should it explode.
And why risk the wiring harness (which can "total" your car, should it cause a fire)?
DISCONNECT THE BATTERY. (I believe my Haynes Welding Manual gives the same advice).
Good luck.