In TWOK, right after the Enterprise destroys the Reliant’s crystal, there is this bit of dialog:
JOACHIM: They've damaged the photon-control and the warp drive. We must withdraw.
So based on that one bit of canon info, the crystal had nothing to do with the impulse engines, despite it being right above them.
But later Joachim reports "impulse power restored", implying it has been damaged in the attack too.
I always assumed that "impulse deflection crystal" implied that it is involved in deflecting power from the main warp intermix chamber into the impulse engines, but that the impulse engines also have their own back-up power source.
Probably fusion reactors - the fabled "auxiliary power". After the Reliant retreats and the Enterprise begins repairs, Spock reports: "Engine room reports auxiliary power restored. We can proceed at impulse power."
Is this the same thing that Joachim reports is restored, and which Khan judges makes the Reliant "more than a match for poor Enterprise"? But he is under the impression Enterprise is dead in the water after intercepting Spock's "exaggerated" status report.
The Enterprise really has "partial main power" at that point, but Spock confirms that Reliant can still outrun the Enterprise.
Therefore, I think Joachim actually means they've been able to repair the deflection crystal enough to have full warp power channelled into the impulse engines, more than Enterprise can muster.
TWOK establishes three power sources:
- Main power - i.e. warp (and full impulse)
- Auxiliary power - (partial) impulse
- Batteries - just enough to keep the lights on and maybe thrusters - but not transporters
The chain of events is: they both get warp power knocked out early. Enterprise's "main energiser" is out, Reliant's "impulse deflection crystal" is destroyed. But she has enough power to escape, presumably at low impulse using auxiliary power.
The Enterprise is immobile on battery power ("she's not going anywhere"), until auxiliary power is restored and she can limp to Regula at impulse.
Spock's "exaggerated" report that the Enterprise has lost main and auxiliary power.
Joachim reports "impulse power restored", which I'm taking to mean full impulse using main power. They may actually have warp speed at this point, but it is never a factor because Khan wants revenge on Kirk, not to escape.
Enterprise has restored "partial main power" but is still out-gunned and out-runned by Reliant.
The Enterprise engine room is again hit and Scotty needs "to take the mains offline". Presumably they are now back on auxiliary power.
Spock fiddles with some dry ice and disco lights (is this the main energiser?), restores full main power, and the Enterprise escapes in the nick of time at warp speed.
Phew!
