When noise is picked up from microphones other than yours, it will interfere with the sound clarity coming from your broadcast. This means that if some participants are left un-muted, others will find it difficult to hear the music you're playing. Consider muting all participants during the class and explaining why you're doing so.
By getting participants to press play on the same track as you at the same time will inevitably cause a lag between you and them receiving the live stream. Even a few (milli)seconds lag in the music can create a bad experience for participants.