I'm sort of hesitant to accept the idea of Starfleet ships running on a fuel-less power system, even though we do lack references to things like refueling, tankers or fuel shortages (except when relating to impulse travel). Supposedly, antimatter fuel is involved, after all. And while antimatter isn't exactly a naturally occurring substance and indeed might need to be generated and re-generated, it would be a bit odd for the ship herself to be capable of doing that. If she can generate or re-generate antimatter at the rate the warp drive consumes it, why the need for antimatter in the first place? Why not hook up the generators directly to the warp engines?
I suspect that antimatter is necessary for creating a space warp (at least in TOS) thus the whole matter-antimatter engines in the nacelles. In TNG, that's a bit different as it's more about the warp plasma going to the coils although it could be that the plasma needs to a result of a M/AM reaction.
Interestingly, "Booby Trap" has an instance where it appears that the matter-antimatter supplies are regenerated. The ship is expending her supplies faster than normal because of the trap. But what is Laforge's and Brahm's solution? Increase the amount of matter-antimatter fuel being used! But instead of burning through their fuel even faster, they almost offset the drain rate. Perhaps TNG also retained the idea of re-generating fuel...
LAFORGE: Matter-anti matter mixture ratio settings at optimum balance Reaction sequence corresponding to specified norms. Magnetic plasma transfer to warp field generators per programme specs. Commander, we should be going like a bat out of hell.
LAFORGE: Great. Another woman who won't get personal with me in the holodeck. Leah, I want to find a way to supplement the energy supply to the ship and to the engines. Could we alter the matter-antimatter paths?
LEAH [OC]: Theoretically, yes. The system should be able to accept more reactants at a faster rate of injection.
LAFORGE: Then, if we use multiple injector streams, hitting more than one crystal facet, we could do it, we could hold our own.
Leah, you're beautiful. La Forge to Picard.
PICARD [OC]: Go ahead.
LAFORGE: Captain, we've found a way to extend the matter-antimatter energy supplies.