"And if you keep doing that for a hundred years, where would you end up?"
In the middle of a dire shortage of energy and resources.
I think this post and its replies are becoming bigger than they deserve to be... Of course a Dyson sphere is actually more plausible than faster-than-light travel, and by an extremely considerable margin. That doesn't make it plausible, however, and I personally - and this is obviously just a personal opinion - think that no culture would, or could, build one. It seems prohibitively expensive, and it would be very unstable and require constant maintanence. It would also become quite severely irradiated shortly after it was constructed, and since it would be emitting almost constantly in the IR (both back in and to the outside universe) would be slowly cooking the inside of it. Etc. etc. etc.
Obviously you're right; Dyson spheres present what I personally believe is an insurmountable problem to engineering, resource management, resource collection, maintenance, and so forth, but they're still basically problems of engineering and resources, not necessarily physics. Faster-than-light travel, on the other hand, presents what is as certain as we can be an insurmountable physical problem, and all the clever solutions of GR (such as maximally-extended Schwarzschilds providing wormholes, or Alcubierre-type distortions of spacetime) can't help that, because so far as I'm aware, none of them are actually physical. If nothing else, building wormholes out of Schwarzschild involves assuming that the entire universe is, always has been, and always will be, a single maximally-extended Schwarzschild (which is self-evidently false); a realistic Penrose diagram of a real black hole looks very different indeed. Meanwhile, getting FTL from an Alcubierre-type solution involves your ship being a "test mass" (so having no influence on the geometry), and infinitely far from any other gravitating source, neither of which is plausible. Compounding this, both the wormhole and Alcubierre solutions require basically the judicious use of something that would act as a dark energy, but under our control. Which is even less plausible.
So of course you're right. I dont' feel either is realistic, and I do feel that specifically looking for Dyson spheres in preference to simply looking for radio emissions, is probably not going to be helpful. (Furthermore, curiously IR-hot systems that are invisible in visible and higher will be picked up anyway, and will be studied more closely. We have a lot of surveys going on in the IR; it's far more useful than visible.) As you say, this is my own feelings, but ultimately (if you can overlook the unpleasant way I put some of them forward here, which I apologise for) they are at least founded on a level of reason. Of course that reason can be wrong, and can be challenged. I just think I'm right. ;)