Hi James,
I have not personally tried SQLite on an MCU. It definitely seems possible from reading their documentation and searching online for what others have accomplished. I think getting it compiling and providing the RTOS and file system specific calls would be fairly straight forward. I think it could be a stretch in terms of size for these small MCUs. It would consume a large portion of both flash and RAM (see https://www.sqlite.org/footprint.html). Also, performance could be an issue depending on the requirements of your application.
I am also a bit concerned about a comment that says versions since SQLite 3.6.22 do not have large support for SQLITE_OS_OTHER = 1 on this post http://stackoverflow.com/questions/35738578/sqlite-porting-on-freertos-with-stm32. There could be certain features that don't work correctly and would require time debugging and fixing.
Regards,
Tyler