exposed duct and avoiding 3 leaf

Hello. I'm new here but have read a lot and done a lot of research. I'm in the middle of a build of isolating my basement from sound getting upstairs. One question I have developed And could not find any posts discussing it: I have an insulated flex duct coming through the area in which I am constructing my isolated room. This duct feeds the room above. My plan is double layer of drywall with green glue on bottom of subfloor between joists, then isolation clips and hat channel hanging double layer of drywall with green glue from the joists. Should I still encase this duct with a double layer of drywall? This will create a 3 leaf system in some areas, but will the benefit of the double drywall around it outweigh the drawback of the 3 leaves In this section? Thanks for any suggestions... learning as I go.

My apologies. I failed to mention: This duct is between joists, and is 6 inch flex duct so it fits up between the joists and between my hanging ceiling and the subfloor above.

Seal it off as you said. The loss due to 3 leaf is well outweighed by the loss of sound getting through the duct to upstairs.

Thank you for your reply, John. I'm a little unclear about your answer. Please forgive me To clarify: I should or shouldn't encase the duct in double drywall before building the hanging ceiling? Again, sorry for needing another look at my post!

sorry I was a bit vague :) Yes, I'd enclose those pipes as sound will travel down them. There will be a loss due to the triple leaf but not as much as you'd get if you didn't seal them off IMO.

Thank you.