If you have Chromecast-enabled playback software, then yes. Windows Media Player can't do it, as far as I know, but Google Chrome, for example, already allows you to stream stuff. Other software certainly exists as well.
I have my music on a NAS (Synology) and control the playback via a Chromecast-capable Android app (BuhbleUPnP, AllConnect, DS Audio, ...) from my mobile phone. This works flawlessly. The mobile phone only plays the remote control. This also works if the music is on your PC instead of a NAS.

The speaker also has Spotify Connect, so you can select the speakers you want directly in Spotify on your Windows PC or Mac.