Slowhonda is right on. You can run a tire down to nothing, but you just can't go as fast on it.
Talk to Matt, he has the best example. I will give mine. I run DCIII's on my relic and I put 4.5 days on it with no problem( 7 sessions a day, that's 30+ sessions). I ran them without tire warmers for the first 4 days. The first 2 full days were in very cold temps, 27F for the first session each day. At 4.5 days I ran 1:22's on Summit Main. That is my normal pace so it didn't really slow me down. The only reason I changed them was I wore a nice flat spot just off the edge of the tire that made an abrupt change in contact patch as you leaned over. On either side of the flat spot, I could run my normal pace but the transition was a bit hairy. I run an ancient bike with bad suspension and an assload of hp. I beat on the rear tire and they just keep going.
As the tire changed I did make adjustments to how I rode but you should be learning to do that anyway. That's part of learning how to ride on the track. You have to learn to listen to your tires. And I am definitely a mere mortal.