To answer the OP. No, not really. I might drive it at 90% and have some fun on track alone. No way would I really push hard in someone else's car. Maybe if they were billionaire best buddies and did not care about money or if I hurt the car.
I have done a few DEs and I told all the drivers I would let them by as soon as possible before we started the engines. I was out there to have fun in my street car, and I planned to drive it home to Oklahoma the next day, and I had no ego pushing me to stay ahead of them in track prepared cars or a car with twice my HP and brakes.