Had to look this up on Memory Alpha. The base principle for both replicators and transporters is confusingly termed "matter-energy conversion", yet doesn't appear to create matter from pure energy. Rather, it seems to use energy to convert matter from/to atomic or subatomic particles (for replicators and transporters, respectively). During the process, the matter is "energized", and - I'm no expert, but - I'd imagine the subatomic particles in the transporter's matter stream exhibit energy-like properties.

So replicators do rely on atomic matter stores (often recycled from waste or unnecessary items), and I'd still expect the conversion processes to use a lot of energy, but not as much as creating the raw matter.