I think Dougie basically has a forward role on the first unit—he is a right shot and his shot is as dangerous as many forwards. Usually 1D-4F is ideal, but I think Gardiner and Dougie works. Then unit 2 has either Gauthier or Necas as a right shot.
Hamilton might be the best in the business at skating in and picking a corner off the rush, but his shot from distance isn't particularly impressive. The PP is a pretty static situation, at least for Carolina. Ignoring quality of ice time, which is hard to measure, he ranks 19th in PP SH% among defensemen with at least 500 min TOI over the past 3 seasons (
Link).
With that being said, it wouldn't hurt to try. However, I don't know if Brind'Amour will. He had 97 RS+PO games to try Faulk and Hamilton on the PP1 after an encouraging preseason last year, but didn't break it out in a meaningful way until game 96, IIRC.