Does hay crumble?
Does grass? Yes. Isn't hay basically dried grass? Then it will decompose eventually, probably wishes contact with moisture at the right warmth.
Yes, hay decomposes slowly, when moisture is introduced. Slow breakdown of this hardy plant is what make it such a good entrant for mulching over wet areas that folks must walk on.
When baling, moisture on the inside of the bale cause bacterial decay, cause the hay bale to become very hot. It can lock in on fire.
Answers: yes