[jakobnev]

Yes but heating does not increase the mass. If you don't send more mass airflow over the turbine, do you think it will perform better?

It will totally perform better, even if you don't have more molecules of air, each one of them is going faster and can deliver both more momentum and energy. (If mass was the only thing that mattered⁽*⁾, gas turbines would run just as well on water as they do on fuel.)

perhaps this engine as part of a hybrid system could work. the electrical side could account for quick power adjustments, given the likely sluggishness of a turbine throttle.

Even if flow control turned out to be sluggish this could easily be compensated for by an extra bypass and restrictor for increasing and decreasing flow faster.

*⁾ No pun intended.