Nearly all of it is driveable, I've driven about half of the route myself, Joplin - west of OKC, the section in L.A. metro, and Flagstaff - east of Amarillo.
The route 66 guidebook by Tom Snyder is also an excellent resource, and I'd pick up the various free flyers and guides available locally at the motel or nearby chamber of commerce that you're staying at.
See it while you can, every year, another motel or building or sign disappears. Two weeks is plenty, but if you're taking side trips to Santa Fe or the Grand Canyon or Vegas, I'd allow some more time.