OK, April, the answer I got last night was similar to many of the others' above:
Yes, the Marines might take him without worrying about the impending jail sentence for non-support. The recruiter suggested that you support your ex in joining the Marines, but, like SparkPlug said, you would have to be willing to state that you could be solvent on your own for the time that he is passing basic. Once he is drawing a salary, you would write to the military, inform them about the deadbeat and your case, and they would begin taking support FIRST out of his military pay. Your son would also be eligible for medical and other dependents' benefits.
It's a risk, as you don't think he could make it through basic, but as you're not getting anything now, and actually, your ex can't make money while sitting in jail, it might be a risk worth taking.
Good luck!
Brenda