It appears that the tray icon cannot be enabled for the 1.0.x client at this time. The issue appears to be longstanding, and is so mentioned at the Spotify community forums: "Linux Spotify client 1.x now in stable"
Regarding bugs/issues in 1.0.23:
Most of these we want to fix, but others (like missing tray icon) we probably won't.
For now, Spotify is not willing/able to devote enough development resources to the Linux client. I have remained on the "spotify-client-0.9.17" package, while periodically checking the functionality of the 1.0.x testing releases (I have both the "stable" and "testing" repositories). The '0.9.17' client is disappointingly flakey sometimes (esp. "Spotify Helper" processes), but it still gives me a tray icon and panel info/support with 14.04.