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OK is I did the search and got my answers.
Traction control off is just that...AH remains on
In comp mode TC is off and AH remains on but with higher tolerances for sliding or drifting the car (like you want on a road course).
Pressing and holding the button will shutoff both TC and AH.
Yes - you've got it!!!
However, I'm not sure you've completely answered your own question.
In addition to TC, there is another function built into the PCM - and that's TM (Torque Management).
When I first read your original question I thought you might be talking about TM rather than TC.
We can control TC and AH with the button on the console, however TM can only be tuned out with tuning software such as HPTuners, EFILive, LS2Edit, etc.
TM was programmed into the PCM to limit power to protect drive train components, and it will pull power on you to do that. If you don't want it, you'll need tuning software (or a tuner) to program it out.
And don't forget the "other" traction control on the car, the limited slip differential.
Electronic TC by the ABS brakes that can be disabled completely and mechanical TC by the clutch type differential that can't be disabled unless it breaks.