Yes, it is possible
This website (which is currently down, I hope not permanently!)
http://www.historic66.com/ has an incredible collection of resources and detailed turn-by-turn directions.
Some stretches I'd personally recommend:
Far western Arizona, from crossing the Colorado River to Kingman. Takes you through some incredible scenery, the old mining town of Oatman.
Then, Kingman to Williams AZ is a step back in time. Lots of nicely preserved and some not-so-nicely preserved motor courts and retail from that era. Now a very local road.
There have been three (iirc) different routings of 66 between Tucumcari (sp?) NM and Albuquerque. These would be worth looking into. The old 66 through Tucumcari is a classic of dozens of western towns with dozens of old motor courts and a town that seems 8 miles long and 4 blocks wide.
Through the northern edges of the Ozarks in Missouri there are often some stretches of the old 66 (in some cases 2 or 3 iterations!) paralleling I44. These are fun to dip in and out of and you would never know you're so close to the interstate.
Two weeks would be plenty, and I'd concentrate my time on Arizona and New Mexico.
<mod hat on -- since this spans several geographic forums, I'm going to move to Travel Buzz from the California forum. cblaisd, Senior Moderator. mod hat off>