Indigestion is most commonly caused by an excess of acid in the stomach. Your stomach is constantly creating acid to digest everything you put in it, although that acid is not strong enough to digest pennies, it may clean them, but I wouldn’t test that theory.
Coke is very highly acidic so adding more acid to a stomach that already has too much acid is not going to help stop the indigestion, although Val may still enjoy drinking the Coke and perhaps that pleasure will make the pain of indigestion bearable. That would depend on just how much Val likes Coke.
It is possible that indigestion be caused not by too much acid, but by too little acid. Water is neutral with acids and bases on either side of it. Both acids and bases can be harmful so if Val’s indigestion is caused by too little acid, and too much base, then drinking a Coke may very well help.