The short answer is , Spotify can download music to your phone, but it doesn't work like a traditional file download . If you are looking for an MP3 file you can move to another app or device, you won't find one.
Instead, Spotify "syncs" encrypted data to your device's internal storage. This allows you to listen to your favorite tracks without an internet connection, provided you stay within the official Spotify app. How Spotify "Downloads" Actually Work does spotify download music to your phone
When you hit that download button, Spotify is not handing over an audio file like an MP3 or AAC. Instead, it saves (Ogg Vorbis format) directly into a hidden folder on your phone. The short answer is , Spotify can download