Constant current LED driver using transistors
Q2 is approaching saturation as the collector is one diode drop above the base. The saturation region begins where the collector base diode becomes forward biased.
Just what constitutes forward bias in a transistor is somewhat subjective; the junction will start conducting at quite a low voltage.
If the programmed current was high enough to cause Q1 to heat up significantly and lower the base emitter voltage significantly, (the device has a negative temperature coefficient of -2.1mV per degree C)  then Q2 (which would not heat up as much unless it was in thermal contact with Q1) would more closely approach the saturation region.
It is highly unlikely that would have any significant effect on the operation of the circuit unless Q1 got really hot (where you would choose a different transistor anyway).