YES, this is good. "If you can HEAR it, you can PLAY it". (that wisdom comes from an old Black Jazz Man...and his lesson is good). If you have the confidence to SING the notes, playing them on an instrument becomes easier. Thank you for that warm up exercise and best wishes for you and your students.
As far as singing blowing and playing it is not about being Black it's about the correct playing concept. This concept was introduced to Japan by members of the Chicago Symphony. Mr. Herseth and Chicowicz Mr. Jacobs all taught these concepts to the band directors and they in turn taught their students the fundamental concepts of tone production. it goes back to George Mager and Ramond Lafosse teachers at the NEC conservatory of music in Boston.