They do not check your BMI, but they weigh you and place that on your long form. If you have a certain BMI, they have you fill out some questions regarding your sleep habits, basically to see if you have sleep apnea. Since you have sleep apnea, I would just tell them up front. They'll install an inverter for you (you lucky dog, makes me wish I had sleep apnea) so you can use your machine. I'm not sure how they'll address that when you are on the road with a mentor though. They might install an inverter on his truck as well.
They will to another physical on you though, and check your blood pressure.