It probably will not help. The circulation of air is outlets at the registers and intake at the returns. You probably don't have a return in the basement and if you don't then there should not be a way for basement air to get into your ductwork. If you do have a return (intake) register in the basement evaluate if your upstairs returns are adequate for the supply and you may be able to close off the basement one.
Musty air is often residue in the ducts. Sometimes good filters can make a difference.