If the songs are not stored locally, they would need to be downloaded and that relies entirely on the speed of your network connection. While you may have a 1Gb plan from your ISP, it's possible that your connection to Dropbox is slower. Regardless though, local files don't have to be downloaded and wouldn't take a minute to load to a player. If it's grey within rekordbox, it hasn't been uploaded from the source, so there's conflicting information there.
No, you shouldn't use XML to sync libraries across drives, you're better to use a drive cloning app or a utility to check files for differences and sync the contents rather than using XML as it's not for that purpose.