I had a 1986 Ford Mustang with 5.0 liter V-8, which I bought in 1993 for $2000. What a rustbucket! It was a big project, only reason I bought it was the mag wheels and tires on it was probably worth what I paid for it. A/C was dead, stereo removed, dash all cracked, rusted out rear hatch. Found out the overdrive band in the AOD was on it's last legs as would hear a scraping sound when it engaged. Bought it from a guy name Marquis DeSade so what do you expect? Funny thing is the engine, with 110,000 miles did not eat a drop of oil.
I did a lot of rust repair on the car where I cut out and replaced the rust with new sheetmetal using a fluxcore MIG welder. Back then, I always disconnected the battery when welding on it. However I forgot to do this on several occasions, and nothing happened. I did about $25K worth of autobody work on that car, if you had a pro do it.
The new cars these days do all kinds of funny things when you disconnect battery power so sorry, your guess is as good as mine. You may want to ask around at your local autobody shops.
More than likely you won't be TIG welding on the car as it's used for finesse work. Most work done on mufflers is arc but MIG gives much better welds.
2013 Ford Mustang GT Premium with Track Pack (11-14 MPG)
2016 Nissan Versa Note SV (36 MPG and climbing)