Stated in dialogue, no. Visually, they used a holder for the crystals (the top that Spock lifts off) that contained something reflective inside which in "The Voyage Home" they show us a close-up of a similar looking holder that held the Klingon crystals (which was identified as such in the movie.)
(click to enlarge)
NOW...I do see and do assume to understand what you are / were trying to say with your "energizer room" theory.
Short and straight answer: This is the Star Trek II main energizer room!
First things first:
gets hit, Scotty reports "main energizer is out!"
Switching to "batteries" will provide them with "auxilary power in a few minutes" which also enables them to have "a few phaser shots" (and the capability to beam several people down to the Genesis Cave, I should add).
Back on the ship Scotty reports "energizer is by-passed" and that's it.
Obviously, my official movie novelization from Vonda N. McIntyre (based on the screenplay) had to take over:
"What's the damage, Scotty?" - "Admiral, I canna put the mains back on-line! The energizer's burst; if I try to gi' it to ye, 'twill go critical!" - "Scotty, we've got to have main power! Get in there and fix it!"
That may not be dilithium-solid evidence, but for my taste I'd consider this to be pretty much rock solid.
Interestingly, the ST II engine room set up is more compatible with the TOS one than the one from TMP as my working premise, too, had been that the dilithium crystal converter assembly is not (yet) part of the "warp core" (movie lingo: "(intermix) chamber coil") but an adjacent component.
And that thingy Spock is working on shares a distinct design similarity with the TOS dilithium crystal converter assembly (it probably retracts into the floor for operation, too).
Khan really knew where to hit them and hard.
I also have to admit that the ST II energizer room reminds me a bit of the TOS dilithium crystal regeneration room from "The Alternative Factor" (i.e. if I were given the job to make a movie version of that room, it would probably look a lot like this one in ST II).
But I still do believe it's just the regeneration room. Given he context of the episode (a possible invasion into federation space), Kirk is rather upset when he learns that the dilithium crystals are not in top shape ("Re-Amplify, immediately!").
Orbiting the planet (and having transporting power thanks to the "batteries") the ship doesn't need the dilithium crystals, yet, thus Kirk understandably wants to see these fully regenerated so that he has full "crystal power" in case he will need it soon at which point of time the crystals will - of course - be put back in their converter assembly "cages".
IMHO, of course.
P.S. These latest posts really made my day! I take as conclusion that the proper designation of the TOS engine room floor casing with the dilithium converter assembly is "energizer" and these big GNDN props are probably the "batteries" or - in my world - fusion reactors.
Didn't I previously mention a rather insubordinate attitude of Scotty in "Elaan of Troyius"?
Kirk gives Scotty a clear and precise order. Apparently, the movie producers became aware of that and decided to let Scotty rather faint than disobey a direct order...