I guess it would depend on how full the flight is. I have attempted to volunteer several times and the FA had said they would have nothing to offer me since I was an F passenger. I told them I was on an elite u/g and if they needed me I was willing to accept the normal compensation and fly coach on the next flight.
If you are DENIED boarding, I think they would have to put you in the same class on the next flight. If you VOLUNTEER, I think they would try, but it would not be required. Many times there is not F available only an hour or two before the flight due to all the free U/G's.
However! I think with NW being a customer friendly airline that if you volunteered for the bump and were not U/G on the next flight, you could contact Customer Service or WP and explain that you helped them by taking a bump and would appreciate them returning your miles that were not used for an U/G. I think you would get them back as a courtesy even if it is not a requirement.