What I can say for sure is no one at Tesla has the time to "GPS track your car" to figure out if you were on the track at some point. Quite frankly, most of those technicians don't care they just want to fix your car and get it gone.
They aren't going to GPS track your car. But when you have an issue and schedule service they check the vehicle logs. When I was getting warning lights for most of the driving systems being disabled a tech emailed me and asked for a time frame for when the issue happened so he could remote into the car and check the vehicle logs. He was able to diagnose it down to an issue with the front passenger side wheel speed sensor without the car being in the shop. Turned out a wire on the wheel speed harness had rubbed on the drive unit and would occasionally short out.
I don't know how long the logs are stored with the car or if any information is flagged but they can definitely see how the car is being driven when an issue occurs. If they see that the car is going from 120+ mph down to 40mph followed by several hard accelerations and braking inputs with the traction control activating in track mode multiple times over 20min it's pretty easy to see its being tracked. With all the information the car is always taking in and logging I wouldn't be surprised if GPS data was logged.
The warranty specifically says that racing and track use are not covered under warranty.