Is it right that the 2.0 TSI engine can handle more power than the AXX etc?
A K04 upgrade on the mk5 GTI puts the engine on about the safe limits.
Would a TSI engine be able to cope with a K04 Hybrid with an aggressive map?
I can only go by experience here.
However I believe the AXX to be stronger than the BWA. I have a personal friend been driving around with an APR Stage 3 kit on his car. It's been fault free for almost 2 years now since It's been installed. travelled around the 40000km's already. that kit is making 245kw's at the front wheels so approx 380Hp.
The new APR K04 kit for the MK6/scirocco/EOS TSI engine makes a claimed 366hp. I see no reason to doubt claims. As my APR Stage 1 GTI (even when it was Stage 2, Never got to dyno it for Stage 2+) is on par to their claim
So in short I cannot see why a K04 Hybrid would have issue's running on the TSI engine.
I do recommend gathering sufficient information, before you decide what you want do.