Hi, besacier,
I walked the Vdlp in May during the 2010 Holy Year. There were very few people, and the thought was that many people had put off their Vdlp because of the fear of overcrowding. Even so, there were usually people around at night. I only remember one night when there were only two of us in a big albergue north of Zamora. Other nights we had company -- lots of Spaniards and Germans, with a few other nationalities sprinkled in.
This past spring, things were very different, I believe. If you look at CaroleH's posts from May-June, you'll see that they fled the Vdlp for the Ingles because of the crowds (I think that's right, but check our her own description). The route is getting much more popular, I don't think it can accurately be called a solitary route any more. Not like the Camino de Madrid, or Invierno, etc.
People living along the route say that the highest spikes in traffic are right around Easter, whenever it falls. I started on May 1 in Sevilla, and it was absolutely lovely through Andalucia and Extremadura. Springtime in those places is amazing -- carpets of lots of different wildflowers, lots of babbling streams, it's a real joy. All the best to you in your planning, Laurie