As I understand it: The GMPP tune (on a manual transmission car) does not completely remove torque management. However, it raises the maximum allowed torque to a level where you will never top out anyway, on the stock turbo.
The GMPP tune does leave in place a couple engine protection protocols that some aftermarket tunes reduce or remove:
1. Max Turbo RPM: If the ECM calculates the commanded boost is resulting in the turbo spinning to fast, the ECM will intercede and reduce boost command.
(I have the GMPP tune on a manual transmission car, and I have observed this phenomenon. I live at high altitude and on a hot summer day the ECM has to to command a butt load of boost to compensate for the low ambient air density, while at WOT. In these conditions, the turbo will get to spinning to fast, so the ECM protection protocol kicks in and the ECM opens the waste gate a little to slow down the turbo)
2. Max Manifold Absolute Pressure allowed: If the ECM reads Manifold Pressure as exceeding maximum allowed threshold, then boost is reduced.
(I have never observed this protection protocol. And I have not read of anyone else observing it either. I suspect that this threshold is set high enough that it does not come into play on a stock turbo manual transmission car.)
The system is Torque based. In OEM format (no GMPP tune or aftermarket tune), the ECM absolutely "learns down" to the maximum allowed peak torque of 260 Lbs. I have personally observed this. Any mods you do to a stock car will learn back down in a few key cycles. The most you end up with is maybe a little quicker spool time on the turbo, but peak torque is quickly learned back down to the 260 threshold.
Now, as far as your examples:
1. 2.0 + GMMP = 290 HP (340 Lbs of Torque
2. 2.0 + GMMP + GM Performance Exhaust = 290 HP (340 Lbs of Torque
(Not because the ECM "learned down", but because the "Performance Exhaust" doesn't really add performance, just noise.)
3. 2.0 + GMPP + GM Performance Exhaust Solo exhaust + GM CAI = 290 HP (340 Lbs of Torque
(Not because the ECM "learned down", but because the "Performance Exhaust" & "Performance Intake" don't really add performance, just noise.)
The only proven mods that actually increase performance are:
1. Additional Tuning
2. Aftermarket IC
(May result in additional torque if your elevation is high enough that Boost Command is peaking out at the top of the efficiency range of the stock turbo. Known as "high altitude syndrome". The stock IC has about a 1-1.5 PSI pressure drop across, therefore the turbo has to run 1-2 PSI higher to compensate and deliver the commanded boost. With an aftermarket IC that does not have this pressure drop across, then the turbo PSI can drop accordingly; thereby getting the turbo back into it's peak efficiency curve. So you end up with an increase in peak torque available.)
3. High Flow CAT or CATless down pipe.
(Has been reported to increase HP by 20ish and increase torque closer to 30ish)
4. Replace OEM Turbo with larger and/or newer technology Turbo, along with new tuning.
(Now you are officially going big. You will quickly reach the max HP and Torque you can run on OEM engine internals: 400ish HP and 400ish Torque)
Sorry that wasn't a yes or no answer.
Edit: (GMPP tune and automatic transmission car)
If automatic transmission then 290 HP, but torque is limited to only 325
(It appears as though GM did leave torque management in play and reduced for the automatic transmission cars. If so, then I suspect that the automatic transmission cars still have "learn down" in play and therefore would have to go aftermarket tune to realize any gains. Someone with an automatic and GMPP tune will have to comment.)