Spotify Connect will eventually be available in Spotify's desktop client, which would be the easiest way to use your laptop as a headless player. Unfortunately I can't wager a guess on when this will be released, but since the Linux client has maintained feature parity with Mac/Windows, it's fair to say that this feature will find its way to the Linux client as well.
Until then, your options are somewhat limited. There are many Spotify remote control apps for both iOS and Android, however these apps usually install a helper program installed on your desktop computer, and I've yet to see one which supported Linux in this respect.