The paper that calculated the rough size of the object that could be pushed by one of these random pulses was fascinating and was posted to Hackers News a few months ago, but I'm struggling to find it. I would like to read it again, and would appreciate if anyone has the link.
The gist of the paper was that these beams would be plausible to push an object in the order of magnitude of the size of a spacecraft. But the calculated energy levels of the emitter (as we observe it) would require something like a dyson sphere, which would mean that if it were actually a light sail emitter, we'd expect a highly sophisticated civilization.