Sync large amounts of data between mobile app and webserver
This is a complex question, as the answer should depend on your constraints:
How often will data change? If it is too often, then the snapshot will get out of date really fast, thus apps will be effectively updating data a lot. Also, with the big volume of data, an application will waste CPU time on synchronization (even if user is not actively using all of that data!), or may become quickly out of sync with the server - this is especially true for iOS where Applications have very limited background capabilities (only small window, which is throttled) compared to Android apps.
Is that DB read-only? Are you sending updates to the server? If so, then you need to prepare conflict resolution techniques and cover cases, in which data is modified, but not immediately posted to the server.
You need to support cases when DB scheme changes. Effectively in your approach, you need to have multiple (initial) databases ready for different versions of your application.
Your idea is good in case there are not too many updates done to the database and regular means of download are not efficient (which is what you generally described: sending millions of records through multiple REST calls is quite a pain).
But, beware of hitting a wall: in case data changes a lot, and you are forced to update tens/hundreds of thousands of records every day, on every device, then you probably need to consider a completely different approach: one that may require your application to support only partial offline mode (for most recent/important items) or hybrid approach to data model (so live requests performed for most recent data in case user wants to edit something).