I am only speaking for Hawk here but you needn’t worry. All the required systems will still be fully available. Hydraulics, electrics, avionics (such as they are in the T1 - the T2 has an APU and hence all avionics would be available after a short delay) would all be available via back up systems.
The engine at idle does produce a minimal amount of thrust but not enough to really notice. A ceased engine may produce more drag but a windmilling engine would not.
All of this means that the aircraft will still fly and, whilst performance will not be identical, the practice will be very similar to the real thing.
The techniques and rules will be exactly the same. Instead of a go around decision at 500’ it becomes an ejection decision. The minimum speed that pilots fly will provide enough energy to level the aircraft and eject if initiated at the correct point.
BV