Yes, you will have to do two operations.

How Plug & Play helps is on accessing the aggregate custom_json data that your dApp deals with, using PostgreSQL tables/views and customized API endpoints.

So you won't have to stream blocks to get those custom_json ops or run your own server if you don't want to.

Without Plug & Play, you will have to stream whole blocks from the first block that your app started, using a library like beem, to populate your own tables and spin up your own server to avail API endpoints.