It should not affect the Pilgrim House and staff at all. There will be a relatively greater distance between both sites. But, overall, things will work out. I know from speaking with both Faith and Nate while I was there as a Voluntario in July-August this year that they are meeting regularly with the Pilgrim Office and Cathedral management to discuss how they can best continue their symbiotic relationship.
Most folks do not realize it, but despite the fact that both organizations, Pilgrim Office and Pilgrim House are wholly different entities, coming from different Christian faith based organizations, they actually work together very well, every day. Each provides something the other does not.
When I was serving there, I came to reply on their kindness and generosity nearly every day. They helped obtain needed items for needy peregrinos, accepted donated items, from walking sticks, hats, clothing, and rucksacks, all the way up to bicycles. As their mission is to support pilgrims, whereas the Pilgrim Office's mission is to welcome and document pilgrims when they arrive at Santiago de Compostela, their differing foci are compatible and complimentary.
I am certain they will continue to work well together into the future.
I hope this helps.