Not quite true. He tried to use that for the draft, and it was refused. This is because it is not unusual for CAs to be drafted, they can fulfill many roles, such as medics. This lets them serve without violating their oaths or beliefs.
On 17 November 1917 the paperwork arrived allowing him to file with the military as a CA, but he refused to sign it. During the time between being called up and then, he reached a decision that even though his religion was against war, he felt he had to answer the call.
I knew I had plenty of brothers back there that could look after my mother, that I was not the sole support, and I didn't feel I ought to do it. And so I never asked for exemption from service on any grounds at all. I never was a conscientious objector. I am not today. I didn't want to go and fight and kill. But I had to answer the call of my country, and I did. And I believed it was right. I have got no hatred toward the Germans and I never had. - excerpt from Alvin York's diary
"The Diary of Alvin York" by Alvin C. York
He was very famous. But like so many war heroes, his fame has grown feint over time. If not for the movie based on his life (with Gary Cooper playing Sergeant York), most Americans would probably have forgotten him as well.