Is there a mod that does that or has it even been attempted? Is it even possible? I feel that the addition of Solstheim in TES: III (or even mods like Tamriel Rebuilt) feels organic because you can literally travel there in game. It would be great if we could emulate that cohesiveness in Skyrim.

Putting cities into the main Skyrim worldspace is possible (but certainly not easy) because the cities are child worldspaces of the main one. This is not the case with the Solstheim worldspace.

Most likely impossible, even with advanced knowledge of TES5Edit. The cell coordinates alone would be enough to stop any potential effort to do this.

With the "Island Fast Travel " mod, you can fast travel to Solstheim.

Unless you also had some kind of real time sea travel thing going on, I don't see the point.