Nope. You can use AirPlay to stream music from other services (like Spotify) through your iOS/macOS device to the HomePod (while using voice commands, if you wish, to that device), but Apple Music can be natively played by the HomePod by issuing voice commands directly to it.

So far, HomePod is looking like a Version 0 product from Apple. Given that it’s not even sold in many countries yet (compared to iPhone/iPad/Macs), it will be a while until it becomes a little more open. Looks like Apple hasn’t yet completely figured out the market and utility for it.