Yes
The efficiency of turbine engines goes up the higher the front to back temperature and also with higher pressure at the compressor discharge (both of which go up with increasing RMP and power) In a geared turboprop like the Garret the pressure (RPM would be the same) but the front to back temp would still increase.
Of course it is that temperature at the turbine that wears em out so quick.
Cheers
Wino