You will be able to hang out with him from the time you arrive until he starts the instruction portion of the day, then again after instructions until he starts turning laps.
When you arrive you're led into a room where he gets fitted for a driving suit and you get an overview of the day from the instructors. You're welcome- even encouraged to stay with him through all of this.
Next you will be taken to the track where he will be taken on a tour of the track in a van, and you will have to wait in the bleachers under a large tent (sometimes family members get a van tour as well). After he returns and is given a tour of the car he'll come back to the tent and wait with you until it's his turn to run. All of the safety gear (helmet and hutchins device) is fitted right there, so you can watch that as well.
After his run you can sit with him and watch the other people in his session run, then you go back inside with him for the "graduation", where he will get his speeds, certificate, etc.
They do a great job of making the drivers feel special and the families feel welcome.