Yes, absolutely, and this is going to be one of the hardest tech challenges to solve. I've thought a little about it, and it's probably unrealistic to think that we can translate every single PG statement into a SQLite one, especially when PG has extensions. So we're probably destined to use the local SQLite database for queries we can parse and understand, and forwarding all the others (both reads and writes) to the upstream PG server.
This slightly breaks model of having a local copy serve data faster, but if only the minority of queries use a format that we don't understand in SQLite then only that minority of queries will suffer from the full latency to the main PG server.