Sync is easily achievable, I use Syncthing to go between my phone, dev server and desktop. Other options are the usual suspects, Dropbox, BT Sync, etc.
As for sharing - yeah, you probably lose that. Well, unless you sync a separate DB or something.
You can easily use it in conjunction with drop box or any other file sync program.
it isn't difficult to share a database file for KeePass and you could easily set up a sync interface for it with github
I put my keepass in a veracrypt container and sync it over dropbox, then you can retrieve it on your phone.
That's a tad on the paranoid side since KeePass already encrypts it. If you're using the latest version which has significantly improved the encryption you should have a very good margin of security.
Its a bit of extra work to get my passwords but my entire "internet identity" is stored there so I don't mind the paranoid security.