Yes, it is certainly possible. But I suggest that you follow the routes designated as Route 66 National Scenic Byway. This will take you through some of the most iconic and historic sites, routes and towns, but will avoid the abandoned routes (now just sometimes a dirt road or very poor pavement).
Parts of Route 66 in a few states are now on Interstate Highways because the original route has been obliterated by the interstate. But through most of its route, it is pretty good 2 lane paved roads.
Each state that Route 66 runs through has designated the route as part of the National Scenic Byway system and you can get information from them through their Dept. of Transportation or their Tourism association.
Here's a link to some overall information:
http://www.route66world.com/Here's a link to an interactive map for Rte. 66 in Oklahoma. Most states have something like this as well. Just google around:
Oklahoma interactive mapFinally, I strongly suggest that you visit your local library and/or Barnes and Noble bookstore and pick up a couple books about Rte. 66 and decide what attractions you may want to see.
Have fun. We did this a few years ago. Some things are great, and some are just really sad...seeing how once great little towns and roadside attractions have now become abandoned.
You might also want to rent and watch the Disney movie "Cars". That entire movie is about a town along a 1950's travelroute like Route 66. Then a super highway comes in and the town gets bypassed. This is the whole purpose of the National Scenic Byway program...to get people to re-discover those little towns and gems of Americana that they miss by just travelling the interstates.