Yes, I think so! Hopefully someone will chime in who has actually done the route but this looks helpful (I saved the the 1.8Mb PDF):
It has a bunch of info including routes, maps, elevation profiles, points of interest and more for Old Gorge Hwy, Hwy 14 and I-84 routes. A couple relevant paragraphs:
In certain sections (between Troutdale and Dodson and between Mosier and The Dalles) bicyclists share the roadway with motor vehicles. Shoulder widths vary from zero to five feet. Traffic volumes are generally light, with the heaviest traffic along the Sandy River to Corbett section. Grades are moderate. Other portions are closed to motor vehicles.
Three sections of the Historic Columbia River Highway State Trail are now open, with additional sections under construction. This is a separated, multi-use trail. Bicyclists traveling eastbound on I-84 are encouraged to exit at exit 40 and use the trail between Tanner Creek and Eagle Creek, to avoid the narrow Toothrock Tunnel on I-84. A stairway located at Eagle Creek provides a groove to facilitate pushing your bike up or down. A second section of the State Trail is open between Eagle Creek and Cascade Locks. This leads you directly into the city of Cascade Locks, where you can follow the original HCRH alignment along Wa-Na-Pa Street and Forest Lane (pg. 9). A third section, between Hood River and Mosier, includes the Mosier Twin Tunnels.