Agreed, you should be license in a state of your choice, doesn't matter which one. Take the exams at your school, otherwise the Army will not pay for you to travel to take them. It's not a big deal to go through OBC without a license, but you are expected to have one when you start at your first duty station.
Also there is a financial bonus to having your license before you got o OBC. You are not eligible for your DASP bonus unless you hold a license. This means if you don't have your license when you enter the service, you will only get the DASP for 3 years instead of 4. You have to sign a one year contract each time you get the DASP so if you get your license in September instead of June when you go to OBC, when you get to your last year you will either sign the DASP and be extended 3 months, or work 3/4 of the year and get no bonus. With increases in the DASP under consideration, this could be a fair chunk of money you miss out on.