This is an option yes, however distributing an expension file on the Play Store is not that easy.
There is no guarantee the file will be available when you launch your app, maybe it will be downloaded later. If you want to download it yourself, you must add the library and code your own system (you will also have to display a loader to the user will waiting for the download).
In my case, the SQLite file weights 1 MB. While I agree that it requires double the disk space once installed, I think having 2 MB of data instead of 1 is quite manageable. 😉