While Apple has yet to explicitly support the functionality, one of the components in the newly-announced Siri Shortcuts feature in iOS 12 could pave the way for Siri-controlled playback, should Spotify choose to implement it.
Siri Shortcuts lets users connect certain third-party apps to Siri to greatly streamline voice controls, allowing them to connect app-specific actions to an invokable Siri phrase.
As noted by TechCrunch, the Siri Shortcuts feature includes a "Play Media" intent that will let users summon audio and video media from third-party apps, and could theoretically be used to direct Siri on iPhone or HomePod to a designated playlist or artist on Spotify.
It's not yet entirely clear how deep this kind of integration can go, but it's likely to operate much less seamlessly than Siri controls for Apple Music. The Siri Shortcuts that Apple demonstrated during its WWDC keynote for instance were limited to sequential actions across apps, suggesting the "Play Media" intent is a one-off command that relies on specific pre-made shortcuts to playlists, artists, and the like.
Still, in theory, Siri could be used to play an artist or playlist from Spotify, and then the listener could use the standard Siri media playback functions to control the listening experience. But that's still some ways off Siri's existing integration with Apple Music, which extends to individual interface controls and even artist/genre queries.
The other issue of course is that it all depends on whether Spotify chooses to implement Shortcuts, but the new feature in iOS 12 is at least a positive sign that Apple is evolving Siri toward increased compatibility with third-party streaming services.