No. Hydrow has no features which would allow you to bring in music from external sources. Hydrow is not, itself, a Bluetooth speaker and cannot be connected to receive audio sent by your phone. Hydrow also cannot connect to any 3rd party music streaming services such as Spotify, Pandora, Deezer, etc.
The music that is played during a workout has been specially chosen by the Athlete to match the pace and feel of the format they have planned. While you can adjust the balance between the music and the Athletes voice, there is no way to turn this music off or play different music in its place.
You can always check the "playlist section in the details screen when you tap on any row in the library to see what kind of music will be featured in that workout.