That's the dream! Currently SQLSync wraps SQLite in a fairly heavy weight way as it needs to both intercept the storage tier (to replicate page changes) as well as the mutation layer (to provide the reducer api). I'm interested in making it lighter weight and perhaps a regular SQLite extension you could install into any instance of SQLite.
As for the web integration, SQLSync works with any framework but currently only ships with a React library. Most of it's logic is framework agnostic though.
SQLSync also provides a query subscription layer that is table-level reactive. What this means it that the client API can subscribe to a query which will automatically re-run when any table dependencies change. I'm exploring more granular reactivity, however for many datasets re-running on table change is sufficient when coupled with OLTP query patterns and small-medium sized data.