It was not uncommon in the early 2000's for applications targeting mobile professionals and sales types to work this way, except that instead of SQLite they used things like Notes¹, Jet² and MSDE³. By modern standards these would be considered "tiny mostly static databases" often not exceeding a gigabyte. Instead of connecting over the internet they used serial dial-up file transfer protocols to synchronize with a central database or a mainframe. People would typically download information in the morning, make updates offline and synchronize at the end of the day. A slow trickle of periodic bidirectional updates insured everyone had a reasonably fresh copy of the information they needed.
1- https://en.wikipedia.org/wiki/HCL_Domino