No. The kids can go through basic, or boot, or whatever during the summer between thier junior and senior years. Then they go back and finish their training after they graduate. There is a requirement to graduate HS. If not then the enlistment is null & void.
In this kids case, he hasn't even finished his boot camp. In the words of R Lee Ermey, "he's still a maggot." He doesn't deserve the right to be called a marine until he finishes his training.