Well, to be honest, as interested as I am in the idea, I was hesitant to reply as I didn't want to distract from responses to my posted calculations. But since those have turned up crickets, I feel free to pursue my curiosity about your speculation.
Something has to stimulate the warp nacelles into making the warp field. What that something is is up for speculation.
Gamma rays seem like a strange choice as they are, like you said, just highly energetic photons. And they're part of M/AM, fusion, fission and nuclear decay because these reactions jiggle the protons pretty hard and all light comes from the jiggling of charged particles. And because of the energies involved, those jigglings are violent, thus the photon wavelengths are tiny, thus they are gamma rays. But gamma rays turn back into particles as soon as they're able, especially from M/AM as the energies are so high.
Gamma rays interact with matter only very sparsely as their tiny wavelengths basically requires them to ram head-on into a particle for anything to happen. The only thing that stands still long enough for that are nuclei and nuclei are very tiny targets. The more energetic the gamma ray, the smaller the wavelength, the more head-on the collision must be for the photon to interact. Thus, paradoxically enough, more energetic gamma rays would supply less energy to the warp nacelles. (I've not calculated this, but it feels right.)
So, IMHO, gamma rays seem to be a terrible method of energizing anything. Especially if it's something that needs high amounts of power, like warp nacelles making warp fields. Of course, you could do worse --neutrinos or dark matter comes to mind as worse.
Further, though I will not pretend to be an expert in any way, my understanding is that the amount of ambient gamma ray energy in interstellar space is pretty small. With some research we could probably find an estimate for the amount of gamma ray radiation per square meter received in low Earth orbit. That should give a lower bound on what to expect between the stars.
Still, none of these statements is evidence against gamma photons as being the initializing particle for warp fields. Indeed, I could probably conjure several supporting features of "gamma ray energizers" for the warp nacelles.
Probably the biggest hurdle, from my perspective, is transferring whatever gamma rays are produced in your reactor to the nacelles. Since they don't interact with matter well, I find it difficult to think of a method to direct it. However, once you have high energy plasma, making gamma rays is easy via bremsstrahlung. So maybe directing the gammas made in the reactor is not needed?
What made you think of gamma rays in the first place? And what precisely do you expect them to do? (Those questions might sound snotty but I mean them earnestly.)
The discussion about fusion and lithium cracking is rather interesting. It hangs together well. But I don't buy that the 23rd century would still be using lithium-produced tritium as fuel. Deuterium-tritium (DT) fusion is an ugly reaction. It produces quite a bit of energy but most of it goes to neutrons: ugly, nasty radiation. The only reason we would do it is because it's comparatively easy to do: tritium doesn't like being tritium and will take any excuse to be anything else. It is far better to use a catalysed deuterium-deuterium (CatD) reaction: approximately the same amount of energy is released but a smaller percentage is put into neutrons; plus its only slightly harder than (DT). At least, as compared to proton-catalysed-deuterium (pCatD) which is much harder but much better. So though I totally buy that the author intended the lithium cracking station to mean a tritium breeding station, I don't buy that that's the in-universe explanation.
However, though I can't think of a method off hand, I see no reason why dilithium could not have some property that would be useful for increasing the efficiency of fusion reactions....or, perhaps it's able to take fusion plasma and modify it to be more like M/AM plasma, making it better suited for use in the warp nacelles. This could be the elusive "energizer" circuit. Using a dilithium crystal to increase the energy of a fusion plasma to M/AM specs by sacrificing total plasma particle density? (No free lunch!) And then, from there, the plasma would goto the intermix chamber? Maybe through another set of dilithium crystals?
When I hear the word 'battery', I think of a volume of material that has energy stored in it, an energy that does needs very little coaxing to be released. IE a material that has some potential energy that needs only be given a path for release. Maybe that stored energy is rechargeable and maybe it's not. (Definitions of this feeling get slippery quickly.) By which I mean to say, IMHO, "auxiliary" power is fusion and "battery" power comes from some energy storage medium.
"Battery power" is not likely to be a chemical storage process --neither ion transfer nor oxidization-- or a thermal storage process --big blocks of white-hot metal attached to heat engines. In both these cases the energy density seems too low to do what's needed and still fit within the confines of the Enterprise. That leaves nuclear storage processes --decay, isomers or fission. Any of which might be controlled with judicious use of quantum xeno effects.
Of these, nuclear isomer batteries seem the most promising as they could be recharged. They'd also remain stable without input power. Unfortunately, I know of no method to induce controlled energy release from isomers. Still, it's the 23rd century! They should have a better understanding than I.
Without a highly efficient anti-xeno effect generator, I don't see nuclear decay as giving much in the way of power. Currently, this is what's meant by a "nuclear battery" and it's what's used on spacecraft like Pioneer 11 or Curiosity. But the power density is dismal compared to what the Enterprise expects.
A small, simple fission reactor might work. It'd be best with a xeno effects field keeping its volatiles in stasis until needed. But it could only be viable if the whole thing could also be well shielded within a relatively small volume. Perhaps using critical-fluid uranium-hexaflouride as both core and working fluid? In a three phase thermoacoustic brayton cycle? The problem here is the amount of time it would give you: years instead of days. Of course, special care with geometry would solve that quandary. Again, it's the 23rd century.
Of course, if I'm accepting simple, turn-key fission reactors as "battery power" then a turn-key fusion reactor would work, too. For example: a supersonic shock confinement reactor. Basically, it's a specially shaped shock tube. Once the deuterium gas is going super or hypersonic in the tube (not sure which) it hits a set of mounds mounted on the sides that force shock waves to culminate to the center of the tube. Where the waves intersect, deuterium gas (now plasma) fuses. The reaction is inefficient but probably implementable in the 23rd century... Even so, this seems more like "secondary auxiliary" than "battery" power.
....This post is way longer than I intended.