I think the voice definitely counts as an instrument. And there's no hope for me; I would use my last breath in life to sing. Back in high school the choir director used to make me STOP singing during bus rides because he was sure I would wear out my voice before the actual concerts; I was still singing on the way home (the director's wife sat in front of me on an 8-hour bus ride and could not believe I didn't shut up the whole time!). When I went to All-Eastern chorus, I met 400 other people who wandered around singing to themselves 24 hours a day, who barely stopped singing long enough to chew their food, and I was glad to learn I was not the only one.
It's a real drag when my allergies are bad or I have laryngitis; I still can't keep from singing.
The only other instrument about which I've experienced a similar obsession was the bombarde; but eventually you run out of hiding places to practice in, or you have a baby and have to protect their little ears...sigh.