That's an interesting philosophical question. We can't definitively answer it because the draft DID exist, and the circumstances in which we live today are not particularly similar to those which existed in 1941.
The draft started in 1940, and at first it was based on a number system not unlike the later Viet Nam draft. But after December, 1941, every man age 18 - 39 (the upper age range varied as the war progressed) was in the draft pool. And a large percentage of those were physically able to serve (that is, were not classified 4-F).
The country really totally mobilized. At the peak, from an overall population of about 132 million, 16 million were in uniform. If we assume that the male population of the United States was 66 million, my guess is that about 1/2 of these were of draft age. So, at least 50% and possibly a substantially higher percentage of eligible males were in uniform.
It was essentially an atmosphere in which you were expected by others to serve if you were physically fit. Oh yeah, we had peer pressure in those days, too. You were expected to see your duty and do it. Almost all the men in my high school graduating class went in the service directly out of high school.
We simply don't have that same atmosphere of total mobilization today. For example, we don't ration meat, sugar, gasoline, shoes, and more. The volunteer army has become a fixture in our society. And we are not trying to mobilize every eligible male.
So would we have gotten 16 million individuals into uniform in the 1941 -1945 time period without the draft? I don't know. But those draftees did a hell of a job.
I’ve often wondered about my generation however, the reactions of my fellow Gen Xers, after Sept 11, pretty much alleviated my fears about how committed we’d be to defending the country after an attack. I have to assume the climate and feelings of 18-30 year olds, after the Pearl Harbor attack, was like Sept 11 only sharper and more pronounced, because the threat from the Japanese was far more palpable than the threat of a network of terrorists.
I think, no matter what a bunch of slackers any generation of Americans appears to be, a genuine and serious threat to our collective and individual freedoms, from a foreign military power, will always mobilize us in a manner rendering a draft redundant.