Did JFK play a musical instrument in public?
Seriously, I can think of worse things for a politician to do. Our former Prime Minister fancied himself a musician. He had a "band" and sang... cripes, I sing better than he does, and I can barely carry a tune in a wheelbarrow. He also did a standup routine that even his son was ashamed of.
As for our current PM, he enjoys bhangra dancing, which is fine for the Indo-Canadian club, but wasn't so well-received during his recent visit to India.
So compared to that, a little saxophone-playing seems pretty harmless.