Yes and no. They aren't paying for health care, get housing allowances, and at least part of the time, don't have to pay for food. Despite all this, the starting pay is still 20,000 a year for the most basic of military jobs, which is more than the minimum wage worker is bringing home when they work 40 hours - and the minimum wage worker still needs to pay for basic things. And this is, of course, assuming that someone is just starting out in boot camp and doesn't get any special education to make their pay go up faster. (A lot of people start above minimum, after they get out of boot camp anyway).
All that said, the hours might work out to be less than minimum wage, but it might be difficult to figure out that number when you add in cost for housing, medical, and all the little details (like bonuses for being deployed or on presently on a submarine).