SQLite is the basis for many not too sophisticated local relational storage needs on MacOS (plus it’s free, so Apple doesn’t have to pay royalties). But, and that’s a polite way of saying “no way”: As @BLUEFROG noted, there’s no such thing as “Index SQLite”. It is a relational database management system. How it is used, which tables, indices, etc., is completely up to the application that uses it. You might want to get one of the freely available SQLite browsers just to get an idea what Bear does and what possibly Drafts does.
What’s worse: There is no concept of “files” in SQL(ite). A database stores records. If they feel so compelled, they might split up the information over several tables (which is what “relational” is all about). DT (or any other app for that matter) would have to scramble these pieces together, and it would be at the mercy of the other app’s programmers: If they change the database structure, “indexing” in DT would break.
In short: That’s a dead end, in my opinion.