Hi, Sojourner,
I do think it's likely that you will come across some Spanish pilgrims -- either on foot or on a bicycle. In May I met two walkers (and walked with them till we hit the turnoff for Valladolid and I wanted to spend a day there), and crossed paths with four or five cyclists. But you are right that solitary is the predominant theme. I was glad I had a book with me, and that I found internet in many of the places.
The beauty of the Camino de Madrid is that it offers many opportunities to interact with lots of wonderful people in the small towns along the way. I found myself going into shops to buy a yoghurt or two and then striking up a conversation with the owner. Or go have a cafe in a bar and wait to see who shows up -- 9 times out of 10, they will ask you what you're doing there (I assume that you, like me, will look very out of place in a small agricultural town of 100 people). I loved it. I think I remember that you speak good Spanish, but even if you speak bad Spanish, it's a great immersion course! There are others who prefer the solitude, and there's plenty of that. But if you want human interaction, all you need to do is ask a question or make a comment and you can be sure that people will respond. Many of the people in these towns have lots of time on their hands and are happy to spend time with you.
I know I've said buen camino to you a number of times, but as you're getting down to the wire, here's one more ! Laurie