I registered for the Draft when I turned 18. I began pioneering in 1966 and all I had to do was show my Draft Board the letter from the Society stating that I had been accepted as a Pioneer Minister and they gave me the 4D classification. The 4D was given to ministers of religion and divinity students. My wife got pregnant in 1968 so I had to quit pioneering. But all I had to do was take a letter from my wife's doctor confirming the pregnancy to the Draft Board and they gave me a 3A classification which exempted me from the draft for the time being.
However, if there was a national emergency on the scale of World War II, then it was possible I could be drafted.
Back in those days all young single male JWs pioneered and kept their 4D classification as long as they stayed in the Pioneer service. But if they got removed as pioneers, they could be drafted.
There were several other JWs that I knew who didn't pioneer and served time in prison.
JWs didn't have to go to prison, they could have accepted alternate service and performed work in hospitals or non-military government service. But the Watchtower leadership of that time considered alternate service to be compromising.
I knew one JW who quit pioneering during the Vietnam War. However, he never notified the Draft Board of his status change. The local Draft Board never found out and the guy stayed free and never went to prison. As far as I know he's still an active JW.