Backdoor Recruitment?

As we go into memorial weekend my mind wanders to the naturally to the subject of the military to which an odd thought began to form in my mind.

I wonder what the relationship between changes in tuition to colleges and enrollment rates in the military is?

Could I as a government entity meet a back door goal of increasing recruitment in the military but cutting funding to education and forcing them to increase tuition costs?

Since one of the primary reasons given for service is money for college this option becomes increasingly attractive as tuition goes up.