I'm sure I could find some data fairly easily...
Anecdotally, I've watched recruiters flock to my school which serves primarily the poor and lower middle class. They regularly fill rooms by saying things like "Feel directionless? Feel like you aren't going anywhere in your life?"
I haven't heard of too many people being turned away because of lower scores on the ASVAB. Also, there is nothing wrong with doing your best to better yourself. Think about this question...if there were more options to better oneself, would the military have as many "new recruits?"
The aforementioned message, when offered on the East end of town at the high school that serves the upper crust, doesn't work too well. They'll be lucky to pull in one or two people. Smart recruiters change their message to one of "Duty and Honor."