I picked up my MYLR from Paramus last June. They were late bringing it out to the lot after my appointment time and I caught the employee who was preparing it and putting my name tag in the window. I told her that she was working on my car --she congratulated me, handed me the key cards and said I could look it over and then go inside when I was ready. I spent at least 30 minutes going over it before going inside to make my final payment. It looked like there were lots of other buyers going over their cars inside and out before driving off that day too.
It was a very busy location and I'm guessing that hasn't changed much. I'd suggest you look for your car in the lot before you check in at the front desk – at the very least, you'll get as much time as you want looking over the exterior as you want. And unless you catch a cranky employee, you'll likely get to see the interior before paying too.