Would dilithium crystals be useful in a Forbidden Planet C-57-D hyperspace patrol saucer? The saucer is only atomic powered (probably fusion reaction), and uses no anti-matter fule. It's speed is 17-ly per year (aproximately equilivant to warp 3 or warp 4).
Well, I'm not going to be a smart-ass like everyone else is being... but I'll give much the same answer.
The C-57D does not exist in the Trek universe, so no "trek magic technology" need exist in that world. Dilithium doesn't exist in reality, after all... at least as far as we know!
What is dilithium, in-fiction? Well, that's never been clearly established, either. But my personal favorite version is that, at a certain atomic weight, the periodic table basically falls back into the same pattern the "lower" levels follow... so, after you get to a certain very high atomic number, very unstable material, you find another realm of stable materials, making up a "second" period table within the first... with ELEMENTS called things like "dihydrogen" and "diplatinum" and yes, "dilithium." (that's DI... not "DIE"... a soft "I" sound)
These materials are very rare in nature, and behave "oddly." (Again, this is all speculative fiction, none of it is real!) In the case of dilithium, if you put a beam of strong energy through it (say, a very dense stream of gammas, like a matter/antimatter reaction would cause), it would generate a very powerful electromagnetic potential difference along the direction of the crystaline grain structure... and because of the nature of the higher-order element, it would be very resilient to this energy.
Basically, under this explanation, dilithium is what's used to convert the raw, unmanageable energy from the m/am reaction into useable electrical power.
Later on, with the TNG encyclopedia, a different explanation was created (something about antimatter not harming dilithium... but if dilithium is made from neutrons, protons and electrons, that's nonsense when viewed from a REAL physics standpoint... a positron will annihilate an electron regardless of what atomic structure it happens to be part of!)
So, I personally prefer the old-school explanation that dilithium is what turns the reaction into useable ENERGY which can drive shipboard systems.
(As a parallel, nuclear-powered vessels today aren't driven by the direct heat output of the nuclear reaction. Instead, that nuclear reaction turns water into steam, and that steam drives a turbine which converts that mechanical energy into electrical power. So... heat -> mechanical power -> electrical power. Dilithium, in "treknology," does something similar... but with one less step. "Radiation -> electrical power.")
Now... as for the C-57D... what you need to answer for yourself is this:
1) Does the "Forbidden Planet" universe have the same fictional "extra materials" that the Trek universe does? (There's some indication in TNG-era that it does, by the way... "krellide power cells" and so forth.)
2) Does the C-57D convert its nuclear power into useable energy through a similar process?
Of course, the reality is "it really doesn't matter, does it?"
