Honestly, that sounds absolutely frightening to my ear. There are redis, there is mongo, orient, and plenty of document-based rapid-development databases which will be a substantially better solution than turning sqlite into Firebase.
Yes, you can use data change notification callbacks. It is a cool feature of SQLite, but did you know that their performance is a big concern in a large-scale database (document database grows very quickly by design)? What about COUNTs? Batching operations? Deadlocks? This will go out of hand quickly, because a hammer is used as a shovel here.