It May Not Hurt The Seat's Fabric Or The Padding, Depending On What Their Composition Is. Don't Forget That The Acid Doesn't Eat Through The Battery.
Others are correct that the seat should be removed and cleaned and any acid underneath should be neutralized, too. Those springs will corrode.
Some fabrics and padding can be 100% synthetic (as in "plastic"). I regularly filled batteries when I worked at a dealership and one time flooded some acid all over my pants. I was mainly concerned with getting the acid off my skin and washed my legs off immediately.
Surprisingly, the acid never damaged the dark blue pants nor caused any discoloration. They were made of some type of synthetic fabric (no cotton, wool, etcetera). For all I know they were made from recycled milk bottles or recycled battery cases.
Time will tell.