poly between carpet and particle board?

Planning for underlayment material (actually radiant floor sleepers) to go on subfloor, followed with, in ascending order, Al plates, 1/4″ masonite pegboard, low-R carpet pad, and finally carpet.
One area that will get this floor treatment has a door opening out to a deck that will be used year-round, and snow will inevitably get tracked in onto the carpet through this door.
Because of $ difference between particle board underlayment and plywood or OSB, I would like to use particle board for the sleepers in this door area, but am concerned with possible moisture migration and swelling in the area that will get snow melt on the carpet.
Anyone ever put poly down under the carpet pad to keep moisture away from particle board underlayment? Or am I just being too anal?