Yes, you can water trees to increase its health, but it still wont generate bullets until the 80 turns are up. At least according to the spec.
From the spec:
A planted bullet tree starts with 10 health, then matures by 0.5 health per turn for the next 80 turns up to a maximum of 50 health. Bullet trees can take damage (or die) during these 80 turns, and don’t start producing bullets until these 80 turns are up.
If this is not the case, and trees DO generate bullets early if fully healed, then it's either a bug or the specs are outdated. Somebody please tell me i'm wrong if this is the case, because that would be valuable information