I had the same worry myself, only having my Learner's License as well.
A recruit that is even older than me didn't have a license period and our SGT told us just to remember that before we do anything in the army we'll be trained on it first. You could be professional drivers for 20 years, or never have stepped foot behind the wheel and you'll receive and require the same training.
I would recommend getting some practice in though, it can't hurt can it?