Is it possible to run a webserver on OSMC?

I dont see why not.
I am running a php/mysql webserver on my pi, serving 3 websites.

I dont know Spotify Connect, but i’ve found these:

http://forum.kodi.tv/showthread.php?tid=125147

http://geeks.noeit.com/turn-your-raspberry-pi-into-a-spotify-server/