There is another issue to consider: the anti-war movement. The OTL counter-culture grew out of an inconsistency in history classes in the fifties between ex post facto laws and the Nuremburg trials after WWII. Americans were taught first that ex post facto laws were absolutely wrong. Then later in the text book, Nazi officers were convicted of violating laws that did not apply to them during the war. Or, put bluntly, a young lieutenant was obligated, when asked to work at a concentration camp, to say "this violates the Geneva convention. Take this job and shove it, mein Fuhrer."
So, the Cold War military staffs Europe and draftees are not sent off to war. Germany and Italy were nice places, after all, even if you did have to drill for a possible Soviet attack. The counter-culture will still evolve, with the Baby Boom responding to new music and Beatles haircuts, or dress code changes in general. In terms of drugs, I'm not sure, but there won't be anti-war protests at the 1968 Democratic convention. Another issue, JFK was lenient with the draft for men who had already started families. Would the trend continue in the absence of a war? Could we still have a peacetime draft today?