I've never floated it, but I've fished the Green quite a bit in that area. The biggest problem is log jams. A couple years ago, boaters had to carry their boats around a big log jam just below Metzler / O'Grady Park. As I understand it, the State won't let anyone cut out these jams, so they can be a problem for a long period. I'm not sure of the current status. If the jams are still there, or you don't know, float it with guys that are capable of carrying the boat.
BTW, floating the Green in this stretch is a great idea. Most of the traditional access points between Whitney Bridge and Soos Creek are now posted and inaccessible, especially in the winter when the water is too high to walk the river very far. With a boat, you could hit some fabulous chum fishing, and good steelhead spots.