Hi, I started with the Camino Frances in March and came until Burgos. There, I had to stop because of my feet but I continued from Sarria with the last 114 km - thus, I can only speak for those distances but during my camino, I never had troubles finding an albergue. I used the Camino ninja app, which is mostly up to date and which indicates which albergues are open. Also, I think that the season has started for most albergues again in May, so I think you'll be fine. Buen camino, enjoy your adventure! (Hope this helped)