Yes, Amarok does have very good integration wind sync with Android phones.
However, depending on your choice of DE, you may want to go with Rythmbox, since Amarok pulls in a lot of KDE libs along with itself.
You may also want to check out `mpd`, the "Music Player Daemon". Remote clients for MPD are available, as are clients for live streaming to your Android Phone. You should also be able to find one that will sync up with your phone.
There is this script on GitHub that you may want to try. However, it uses rsync and I think ssh on the device for syncing. I haven't tried using the script in the past, so I cannot take guarantees for how it works.
Since it's a script, you can always hack it up a bit to make the changes you want very easily.
When you say, you don't have an internet connection on your phone, I assume you are trying to imply that the sync will be done through a wired connection.