I'm European so I don't know that much about American politics or history but this is a question that has bothered me for quite some time now. I know about the conscription that ended during the 1960s (?) or something like that so I'm wondering whether American men who were obligated to serve in the military temporarily were also forced to go to war when there was one.
Yes, forcibly conscripted men saw combat in many wars over time. There were limited instances of states resorting to the Draft on the American Revolution, many more in the Civil War. And large nation wide efforts in both World Wars and Vietnam.
In fact in WW2 voluntary enlistment in the military for most men was suspended in 1942, meaning the only way to join was through the draft. This was to better control the flow of men into the force and to balance it against evolving needs and drains on the economy.