Doable, but will require quite a lot of paddling.
Standard pace w/o motor is 5 or 6 days (potential rest day) from Green River to Mineral Bottom, and 2 or 3 days from the Confluence of the Green and the Colorado to Hite. I'm not sure how long it takes from Mineral bottom to Confluence- haven't done that section.
The lake level is up at Lake Powell- so the last part of the trip may be a bit brutal if you don't have a motor. No current after.. Gypsum canyon I think is the canyon name. No convenient camps for the last 30 miles or something.
Have a great one!