Hi.  If you mean downloaded in the sense of ‘offline content’ rather than purchased outright, then yes, you need internet.  DRM restrictions imposed by music service providers generally only allow ‘offline content’ to be played on the device on which it is stored, nit third party systems like Sonos.  That is certainly true of Apple Music.  When you play offline content from Apple Music on Sonos, the music is actually being fetched from the internet.  So no internet connection = no go.

Further thought… You should be able to play offline content to a Roam using Bluetooth, but I don’t think you can play to a pair of Roams usng Bluetooth.