I didn't bring the hammock on the Camino since there were two of us hiking together, we carried a Hubba-Hubba tent. However, I kept thinking that if I were going solo I would have carried my Hennessy. I hiked the entire Appalachian Trail with it and we became very good friends. I emphasized that in my book about the hike.
At the eastern end of the Camino, we started at Ste. Jean Pied du Port, the terrain is not very level at all and there are plenty of trees, perfect conditions for hammocks. The meseta on the other hand doesn't have much forest, but it did have lots of "islands" of clumps of trees.
The problem we had camping was that there are three choices on the Camino:
o a public campground, which usually cost more than an albergue and were usually far from the Camino.
o Camping at an albergue, some did let us, but that was hit or miss. They would charge the same fee, but it was nice to have the showers, community, etc.
o "Stealth" camping. This is where you go off into the woods and set up for the night. Since one never knows who owns the land, that is always "iffy," but as long as one is environmentally responsible and goes deep enough into the woods, should work.
Would I carry the hammock? Certainly. How often will you use it, I guess that depends on how aggressively you like to camp. One downside: you'll miss the sense of community and gathering of peregrinos every night--unless you're camping at an albergue, and we REALLY got to enjoy being with the others as we formed friendships.