So keeping in mind that i did this both times in March when it's likely quieter...
Generally, I'd say no. The traditional albergues (so the municipal/parrochial ones) don't normally take reservations anyway -- it's first come, first served. Even in Holy Week (when everywhere is really busy cos lots of Spanish people do bits), I had no problems.
I would say though that one place it is worth booking is Roncevalles/Ronceveau because it's in the middle of nowhere and after going via the Pyrenees, you really don't want to have to keep walking if there are no beds left. (The albergue is big but when I was there, a load of coaches turned up and then it was full.)
You may also want to book at StJPP if you're going to arrive late as think it's generally pretty busy.
Anyway, I think booking is a bit rubbish as then you HAVE to get somewhere. And some days you may be up for walking more/less, depending on how you're feeling. And you might fancy hanging out with some of the people you meet en route too.
It apparently gets busier from Sarria on but I haven't made it that far yet.