What? Of course the apparent affect matters. If the underlying physical principles can be understood, there is a possibility of increasing its efficiency for larger throughput. And if the underlying process isn't understood, there is no way to rule out something that isn't actually producing thrust or some other fluke.

Finally, the whole point of science is to discover things. Not make magic :|

It would matter a great deal. If it was just radiated photons a la the Pioneer Anomaly, that's pretty boring. Yes, you can make a drive that runs on pure energy by shooting photons out the back. This is well known, and not very interesting. A flashlight is a really, really, really low-powered rocket. But the thrust you get out for the energy you get in is extremely small, and there's no way to improve on it with the same principle beyond increasing the efficiency of the system. Energy->light systems can already be built with 80% efficiency or better, so there's not much headroom.

What would make this phenomenon interesting if it actually works is not merely that it requires no reaction mass, but that it's much more powerful than a photon drive. If it turns out to just be a photon drive, then the magnitude of the effect has been greatly overstated, and this is a really complicated way to achieve the same effect as pointing a laser out the back of your spaceship.