Welcome @Jgulledge
Putting the databases on an external drive is fine, but @OttmarKlaas is correct that you should close the databases - and also properly eject the drive - before disconnecting it.
However your discussion about syncing is unrelated. Sync data is not your database. So could you sync to a local sync store on the external drive? Yes. Is that the same as working with your databases from the external drive? No. They are not the same thing.