As long as you're willing to pay for treatment for the sexually transmitted disease(s), too . . .
Actually, as the mom of a 19 year old male, I can really understand your wife's viewpoint. She spends 18 years trying to raise him with values and respect for women -- and you are condoning an act that is, ultimately, supremely contemptuous and disrespectful of women because you are telling your son that, basically, it's ok to use a woman for sex. Not only to use a woman for sex, but it's ok to PAY her for it, even though she is probably basically a slave to her pimp.
If he's going into the Marines, he'll get laid soon enough. He doesn't need his parents sending him mixed messages with regards to how he should treat women.
If you want to spend quality time with him before he goes in, go skiing or sky-diving.
Besides, how do you know he hasn't gotten laid, yet? :-)