"Pottery" tends to assume ceramics. In Neolithic and later sites that had pottery, ceramic remains typically represent 99% of the total artifacts.
Bronze age tel sites are littered with ceramic pebbles. Every pot eventually becomes a bunch of shards and pebbles that last forever.
That said... a material culture that only uses ceramics occasionally wouldn't leave such signs.
Also.. you could call a wood or hide bucket "pottery," I think.