Parrochial Albergues - will they accept transported bags?

Yes, many albergues accept the bag, but will not assign a bed place until the Pilgrim gets there. In addition, there are drop-off points in almost every village and town, from where you can just pick-it up and head out to the albergue of choice. It is a popular choice to use a transport the first day SJPDP-Roncesvalles. The bags are dropped-off at Albergue La Posada whether you are staying there or not. The company will provide you with a small day pack that you return upon picking up your bag. In the ancient days, churches along the Camino used to provide transport help with young lads who will then walked back helping other pilgrims (remember pilgrims used to walked to Santiago and then WALKED their way back home!).

Every transport company has a website and there they list the places they deliver to/from in every town and village along the Camino(s). I used transport services many times, no complaints whatsoever with Jacotrans.

Some do, some don't. It's best to call ahead and make sure before you send a bag anywhere. We had bags arrive at Albergue San Anton, and we had to send them on ahead to a safe place at Castrojeriz. The bag owners arrived later, and were very unhappy.
But volunteers in a busy, wide-0pen place have enough responsibility without having to secure peoples' luggage.

As others have said, some do and some don't and so it's best to phone ahead. It even depends on the hospitalero in some cases. When I was hospitalero at Parochial at Estella last year, I was willing to accept bags but my fellow hospitalero was dead set against it. I don't know about Granon but suspect they don't. Certainly at Gaucelmo Albergue at Rabanal does not accept Pilgrims who do not carry their own packs. Don't have information on any more unfortunately