Everyone's experience will vary but my experience would suggest that you will be glad if you commit to the entire Camino even at the expense of not seeing other historic and interesting parts of Spain.
It's hard to convey but once you have been walking for a week or more, you become part of a container that is co-created with your fellow peregrinos. That container is one of the most unique and special environments in which to live, and (again IMHO) much more rewarding and valuable than "just another sightseeing vacation," no matter how interesting or incredible the vacation sights might be. Far better to spend as much time in the Camino container as possible now, and make a separate trip in the future for traditional sightseeing.
My $0.02. Obviously not everyone can make time for the entire 5+ weeks to walk the whole Camino. If so doing only part of it is certainly authentic, but I have yet to meet anyone doing it that way who hasn't wished they could have done the entire thing contiguously.