So, the "impulse engines" aboard Enterprise need to be capable of getting the ship to a safe location... the nearest star system, for instance, if you're in interstellar space, or at least away from any hazards in the vincinity. We're talking a pretty significant "duration of operation" requirement... especially since (with the bussard system) you've got no easy way of refueling (and even if you have bussards... at sublight speeds, they wouldn't do too much good anyway!)
If I remember correctly, in TOS "Where No Man Has Gone Before" the
Enterprise was expected to take six months to reach a starbase on impulse power, after the warp drive failed. I don't remember if a specific distance was mentioned, but it was implied to be interstellar.
And that was with the entire ship. Losing the mass of the secondary hull would presumably reduce the travel time.
Marian
Captain's Log: Stardate 1312.9 Ship's condition: heading back on Impulse Power only. Main Engines burned out. The ships Space Warp ability; gone. Earth bases that were only days away are now years in the distance.
Those, along with bits from "Balance of Terror" and a number of shuttlecraft issues throughout the series demonstrates, incontrovertably (unless you choose to delete massive amounts of TOS, I s'pose) that "impulse" can be FTL.
This does NOT mean that "impulse" is not Newtonian, however. It only means that a newtonian "impulse-based" (which is totally synonymous with "thrust-based") system is part of some other form of FTL propulsion besides "warp drive."
When it's said that the "main engines are burned out," this does not mean that the warp nacelles have been destroyed. The fact that they are able to salvage equipment from a MINING STATION to restore the ship to "mostly functional" status demonstrates that abundantly well. And most of what we see being replaced on Enterprise consists of electronics... control systems, in other words.
So... perhaps Kirk's comment isn't entirely accurate, but only insofar as it's "truncated" and slightly incomplete.
His line, if spoken by someone who wanted to be 100% technically accurate, might have been "the control systems for our warp propulsion system have been burned out."
Why does this matter? Well, because the HARDWARE would still be functional, and there is still clearly enough functional computer hardware aboard to permit most ships' systems to function perfectly well.
SO... they may be able to generate power, and divert it into the subspace-field-generation hardware, but not to manipulate that subspace field to be a "warp field" (a subclass of subspace fields, let's be clear).
This is EXACTLY why I've been pushing the whole "static-subspace-field-assisted impulse as an FTL propulsion system" for the past couple of years.
It fits... with everything. It allows FTL without warp drive. It makes the "Bonaventure" from TAS make sense. It lets Jose Tyler's line from "The Cage" make sense, as well as the more "experimental-drive" treatment of warp drive in The Cage to fit as well. It lets the Romulan stuff make sense. It lets the "FTL impulse-only shuttlecraft" thing make sense (and also the presence of nacelles... which generate a subspace field, but not a WARP FIELD... on the shuttlecraft make sense).
Everything works... if you assume that a "static subspace field" can permit limited FTL capability under newtonian-based impulse drive without the presence of actual "warp drive."
Okay, then... here's the thing. In WNMHGB, we have a COMPLETE STARSHIP, not a separated saucer. Granted, it's not able to do the complex and subtle control necessary for manipulation of a subspace field into a safe "warp drive" field. But it still has the ability to generate a subspace field... and it seems to me that a "static field" is quite safe, compared to a "warp field."
So... where is the "static subspace field" being generated? THAT is the real question.
In TNG-era terms, it's safe to say that each subsection of a ship has the ability to generate such a "static subspace field." But in TOS-era terms, there's no reason to assume the same thing.
I assume that the WNMHGB sequence involves Enterprise creating a subspace field (not a "warp field") in the nacelles.
I still haven't decided if I think that the saucer needs to have the ability to generate its own "static subspace field" when operating in independent mode. Yes, it's NICE... but is it practical in TOS-era terms?
In my TOS 1701 work, I've got a couple of places where I've been CONSIDERING putting "field coils" in the impulse housing. Basically, to either side of the impulse housing (outboard of the thrust units and behind the row of three fusion reactors), there is some empty space, as seen here:
What I'm CONSIDERING doing is putting "field coils" in those spaces, to permit the saucer to generate its own subspace field (in emergencies only, after separation!) to make it a practical "deep space lifeboat" without having to be a generational vessel.
Remember, though... in my take on "FTL impulse," the practical "speed limit" is about 75c, and that's at the top end (after that, you get "relativistic effects within subspace"). 75c is, in "Trekkian" terms, the rough equivalent of about WF4.2. So, it's reasonable to say that the saucer, when separated, would be able to sustain something equivalent to about warp 3 for long enough to make planetfall in a nearby system.