Apparently, I will not be able to play the game if I buy just the Special Edition Upgrade. But does anybody know if I will be able to access the soundtrack, art, etc?

There's no way to buy just the SE upgrade, unfortunately. Only purchasers of the game can buy the goodies as well.

There IS, however, a way to buy the soundtrack without buying the game:
https://simonpoole.bandcamp.com/releases

There's also the chance that the music of Books 2 to 5 will be added to the bandcamp release once all Books are out. This WON'T happen for the Special Edition owners on GOG!

As of right now, the music is just about the only worthwhile extra besides the stunning art book, so a bandcamp purchase might make sense. The short stories are running considerably late and have not yet been uploaded.

Oh I didn't notice the soundtrack was only for Book 1. So that street singer-songwriter guy's songs aren't there (and the song from the credits)...

The "stunning art book" sounds like something I'd like to have as well. Surprisingly.

Correct, I don't think they can acquire the rights for Egil Olsen's songs. However, all of these songs were published before, and if that's what you're primarily interested in, it shouldn't be a problem as well.

http://www.egilolsen.com/music.htm

The songs from Chapters are:

Don't just say you love me, show me
Keep movin'
Singer/songwriter

Just look up Egil Olsen... you will definitely find what you're looking for.

Here's a guide for Chapters' music and its availability (I compiled that one, so if there are mistakes, all my fault ;) ):
http://tlj.wikia.com/wiki/Music_of_Dreamfall_Chapters

Thank you very much for the info. I'm a lazy ass for not googling it in the first place.
Putting a real musician in game is an incredible move, goes so beyond just background textures and generic NPCs. Definitely caught my eye.