Yeah, they're called minor Shardworlds, as in they don't have any of the 16 Shards of Adonalsium in residence. Ashyn, First of the Sun and Yolen are examples of that.
Look at the original inhabitants of Roshar: the spren, Greatshells, the Singers. The magics from before the Shattering would be a part of the ecosystem.
When Adonalsium was Shattered, all Investiture in the Cosmere got assigned to a Shard. For example, Ruin's Investiture isn't just on Scadrial, it's spread across the Cosmere. Not all of the power of a Shard is concentrated in one place by a Vessel.
Religions don't all have to come from the Shards. In the real world there are or have been cultures who've worshiped their ancestors, spirits of the land & water etc. Not all religions on Scadrial and Roshar correspond one to one with the Shards either. They might perhaps believe in the God Beyond.