Hi Jordan: Jane and I carried a rather pricey tent (
Hubba-Hubba) on our
Camino Frances. We used it six times and loved it. We walked in Sept-Oct. As a rule, at that time of year, there are plenty of rooms, but we enjoy camping and being away from the snoring. Additionally, I like to throw a wire up in a tree and use my tiny ham radio and Morse code along the way, a tent is perfect for that.
When I hiked the Appalachian Trail I used a
Hennessy Hammock and was thrilled with it. Of course I was alone, so a hammock was perfect. As we walked the Camino I was spying places I could hang the hammock and it should work there as well. We recently hiked the Ridgeway Path in the UK and I would have given my left arm for a tent (we didn't bring one.) Everything was sold out and we had to get stuck with a dumpy little room for 150 British pounds, it would have paid for a tent!!!
If you can carry a really compact tent, you might enjoy it. If you camp "discreetly," you shouldn't have trouble, following all the rules about cleaning up after yourself etc. There are plenty of farms along the way and one can always ask about camping. At several of the alberques they let us camp on their grounds and we then had a food, water and shower source.
It boils down to carrying extra weight, if you can do that, it will work out. If you don't really have the room to carry it, then it may be more bother than it is worth.