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Yes. The graviton in question would be a massive partner to the ordinary, massless one. You get those in Kaluza-Klein style theories with extra dimensions [1], so they are often referred to as "KK gravitons".

[1] https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory

Isn't the fabric of spacetime itself the carrier for gravity?

In relativity, yes. But quantum mechanics people have hypothesized a graviton anyway, presumably with the goal of unifying the two theories.

No that's a convenient metaphor for gravity at large scales.

or maybe particles are a convenient metaphor for small scales

The graviton is expected to be massless, but I don't think there's any information about the particle's rest mass.