...if you think getting socks and underwear dry overnight can be hard at times, you should try getting cycling shorts dry!
But seriously... I've been watching La Vuelta and have been wondering how they deal with things when it 'overlaps' with the Camino. Our 2014 Camino (cycling as it happens) was somewhat deglossed by having a Vuelta time-trial in Santiago the day after we arrived but having all the regalia in the square set-up in readiness.
Finished (walking this time) the Frances route 11 days ago but I can't recall how much of the walk up to Logroño was on the road.
In any case, both El Camino and La Vuelta bring money to the communities involved so I'm sure both are embraced.