It can, especially if it gets wet. Try using a bit of baking soda and give the material a little cleaning with it, that usually kills the acid.

Baking soda will neutralize the battery acid but it will need to be flushed with clean clear water to remove any residual residue. After a thorough cleaning a repair should last and be as strong as the original material.
Also treat the underlying materials at the same time to insure that any cross contamination is eliminated. You would not want to make a repair just to have it fail in a few weeks because of other possible contamination.

A few months back a seat that had battery acid spilled on it came to my shop. Like you said the upholstery was fine but the thread was destroyed. I took the cover off and gave it to him. He sent it out for cleaning and I cleaned the foam. I even covered the entire cushion in 1/4" foam. After sewing the seams back together, the thread dissolved in only a couple weeks. From then on I order new foam and upholstery from the dealership whenever their is a battery acid spill.

Anymore, my routine is with fabric or vinyl covers, remove the seat cover, take it to a Laundromat, wash on gentle cycle, air dry, (DO NOT PUT IN DRYER), ( you can't wash a leather cover) resew cover, glue a thin plastic, like cushion ease or trash can liner on infected area of seat foam, so acid can't wick back up into seat cover, and reinstall seat cover. Like I said, the cars belong to dealers, so I won't see them again. I wish I knew if this is the answer. I feel I have done everything I can do. I don't know what else there is to do. Thanks for the feedback, at least I know I'm not the only one with this problem.

I have a dumb question why is there battery acid on the seat in the first place.

I ask myself the same question every time I have to fix one,

LOL. Yeah, only God knows...

I have never had one touch wood