Absolutely. I've seen it time and again and have done pass runs in various cars with it on and off. My factual data is only real world experience backed by timeslips. Also depends on the car your running. Heavier cars that do not have lots of horsepower are hurt worse by it than lighters cars. I've also seen that V8's tend to strugle more with the AC problem than turbo's 4 or a 6 cylinder. For example a 1996 Impala SS, running 13.56 without air would run 14.76 with the air on at the start. I've know about WOT cutoff but there is enough delay to cause lag, and its not the same for every vehicle.
This is my experience and thats all I can give. Its also fun to see the time sheets on cars raced in cool to mid temps and then run them on a high temp day. Its sad to see the times go up when your car ran so well earlier that morning.
Bill3508