I'd like to think so. My great, great Grandad was a professor of music, he is listed as a musician when he was in the Household Cavalry, and taught flute afterwards as a profession. His son, my great Grandad was a Musician by trade at one point, but I don't know what he played. His son, my Grandad played piano beautifully and won a place at a London Church choir school (which he couldn't take up as his mother was a widow and the family was poor). His sister was into amateur dramatics, singing Gilbert and Sullivan and like music. My father played clarinet, alto sax and violin, playing in dance bands across Leicestershire, and had his own band for some time. My brother taught himself violin up to a point, and played tunes he composed on harmonica. Then there's me: not a musical bone in my body, tone deaf, singing like a rusty nail. We two are last of our line and I don't think our 2 cousins have a musical bent. If it is in the genes it appears to go down one male line only.
On my mother's side, Grandad was a shoe designer by trade, we had his great book of wonderful designs. My mother was a watercolourist and she was very creative, designing clothes which she made, and also made and designed marquetry work. Art was one of my best subjects, my teacher encouraged me to take up[ dress design and commercial art.
Perhaps all a coincidence, but I think it's likely. don't see why, if we can inherit other traits, that we can't inherit certain abilities in the same way.