Always good practice to seal your joints, helps ensure the air gets to where it is supposed to go. Caulking; I assume you mean with a caulking gun, is probably more work than applying duct sealer from a can with a paint brush.
Sealant can hide a few "sins" as well, if artfully applied

We would occasionally use caulking on the small end of round duct connections, so the sealant is hidden, for exposed ducts.
As for insulating, not sure on the high temperature rating of foil covered "bubble wrap" but it is probably a good insulator. Will it last on a hot plenum?
We only ever used foil faced fiberglass duct wrap, 1" or 2" on the outside of ducts (6 of one, half dozen of another?)