That would have been interesting, but the answer is unfortunately no.
The Steve Miller who is Glenn's son was adopted when Glenn was in the AAF, so he had no real contact with his father and had no musical inheritance*. At one point he was employed as a gunsmith.
(*) The musical genes run strongly in the family. Glenn's brother Herb was a trumpeter, his nephew John now leads Herb's orchestra, and niece Wynne is a dancer and entertainer.