Can my databases be set to sync between iOS and MacOS?

Yes, probably the easiest way to do this is to use an iCloud based database. You can create a new iCloud database in both the Mac and iOS versions of the app and it will automatically appear in your other devices in Strongbox. Your database(s) will then be automatically be synchronised and updated automatically across all of your devices.

Otherwise you can use one of the other cloud providers, like Google Drive, Dropbox, or OneDrive. This is relatively straightforward.

You could even store your files locally on each device and manually manage updates and synchronisation via iTunes, File Sharing, Email or URL Import, though this might be a little inconvenient.