MCO P1100.72B states that you can't serve in the USMC as an alternative to prison or jail for a felony conviction. I don't know when MCO P1100.72B was written but I would think that it wouldn't be possible, even for the son of a very rich and influential man.
Dreammaker182
It was very common during the days of the draft, 1950's-early 1970's. During Vietnam. Get in trouble and if the judge thought a little "discipline" might straighten you out, you got the option to enlist in the military (any branch) or go to jail. Of course, enlisting might mean a one year tour in Vietnam, but yes, it used to be very common, and since the actress in question got her Hollywood start in the 1970's, it's not that far out of question.
Once the draft was done and Vietnam was over, people started enlisting when they were financially strapped and needed a steady paycheck. At that time, the military changed their requirements, most of them requiring a high school diploma (not required during Vietnam) and upped the ASVAB minimum scores to try to fill their open positions with higher quality recruits.