It's definitely not pretty (yet) but it is working and that is what is important. Clients can connect and move around the world together. I finished chunk synchronization which required a whole queue system and some other complicated business.
Real-time chunk updates are working as well so if a client changes a terrain tile, other users will see the changes instantly.
Tested Over The Internet
I ran a few tests over the internet (thanks to Panos and Seb) and was surprised to see no issues occurred even with low bandwidth download speeds. Of course I won't really know until the multiplayer is more 'functional' how efficient it is but for now I am more than satisfied.