I hitchhiked together with my wife from Cahors to Orthez in 2012. From there you are on the route from le Puy and can be in SJPdP in 2-3 days, witch can be a good preparation before doing the part to Roncevalles.
As a couple it might be more easy then as a singel man. In general, I like hitchhiking a lot and had a lovely day. We did it in 3 rides, never had to wait more than 30 minutes. Hitchhiking was much faster than doing this by public transport. I would do it again for sure.
So yes, I think it is very well possible if you are flexible and can get along the difficult parts of it (waiting for hours in the rain) and the nice parts (having nice unexpected meetings with lovely people).
These are two sites (of many) to arrange a ride beforehand:
http://www.blablacar.com/
http://www.hitchhikers.org
Have a nice trip!