It's hard to say definitively. If you're issuing multiple database queries per request and you aren't using really complicated Postgres SQL then I would guess that you'll see a performance boost. In tests I've done with Postgres, I see a ~1ms round trip between the application server and database server—even when both are in the same region. If you run 10 queries to serve a single HTTP request then that's 10ms right there.
Hm, will definitely have to look into it then as I’m pretty bad at making efficient queries and use a lot sometimes just have to get over my fear of like, SQLite being only for client and testing stuff and not servers…