Any engine is going to burn more oil if you run it faster. If the engine burns a certain amount of oil per revolution, then increasing the number of revolutions per oil change will cause consumption to go up. I haven't done a lot of racing with my Integra, but it has never shown any oil consumption at all. I've only changed the oil 3 times so far.
'00 Type R #1322 (Yellow)
'86 MR2 (Super White)
"Burning" oil is when your engine (due to inadequate sealing) allows some oil to enter the combustion chamber. When the intake charge is ignited, the oil is vaporized. The result is reduced oil level and excessive carbon deposits in the exhaust path. All engines burn a little oil. The best way to tell your car is burning oil is to check the level regularly and see if it's decreasing. If the oil level is decreasing and you don't have a leak, then the car is "burning" it.