If Henry accidentally drank one of his own pee-filled Gatorade bottles, we'd have yet another instance of barfing to add to a long list in The Art of Fielding.
Henry makes himself throw up so he'll feel better during a game when the pressure is really getting to him. Even though he isn't sick from indigestion, this makes him feel better. Later, when in a fit of adolescent rage Pella swallows an earring on purpose, she pukes it up in a bathroom.
Even though Pella has a more valid reason for making herself throw up, we're told "She'd never really been bulimic" (42.95), even though Henry is the one with the apparent eating problem.
Also, Henry trains Avila so hard that Avila pukes. Henry thinks, "It felt good to make somebody else puke for a change" (31.30). On the very next page, Guert Affenlight almost tosses his cookies after performing oral sex on Owen.
So, if you learn nothing else from The Art of Fielding, you'll learn this: puking can make you feel better. It's a way of relieving pressure.