This article should answer your questions –
Once you have done the test, if your heart rate drift is less than 5%, then the initial heart rate (at the end of warmup and beginning of your test) is your AeT. When I did my test, I had no idea of my AeT. I used the MAF formula (180-Age) to get a rough estimate and then repeated the tests till I got a heart rate drift of <5%.
Training Peaks will not calculate your AeT.
If your initial heart rate for the test is far below AeT, I think your heart rate drift will be much lower.
I hope this helps. Good luck with your test.