Congrats on the new rig!!
We did the complete Route 66 from Chicago to Santa Monica last May and were able to find and drive a lot of the old Route 66 in our 28' Tioga Class C. There were a few times we had to turn around as the road just abruptly ended.
You can usually take the "new" route 66 which is the highway for a few exits to get back on the old road. I would not hesitate to do it again in a smaller or little larger RV. So I would suggest go for it. The worst that can happen is you take the highway and just jump on and off when sightseeing.
Check out our blog where we posted daily our adventures. Along the Way with J & J
Good Luck and have fun!!