If it says HS Diploma on it and the school is legitimate, not a "diploma-mill" then yes. Your recruiter will need to talk to his Education people and request an eval from them, if it isn't in the list they have.
Whenever you are to ship from MEPS, you do a drug test, you should have done your physical aready. I'm just thinkin the Army will make sure you are fit to fight before we give you free schooling.
If you were at my desk, I'd ask what you want to do, the Army has 150+ Jobs, chances are something will fit. We can guarantee your training and let you pick your job while in our office, the other services can only offer a job field or tell you what your job is after the basic training. You...