The EM Drive (almost certainly) either can't possibly work -- any positive results reported so far being more than likely due to experimental errors or misinterpretations -- or, since it already breaks at least one fundamental law of physics, may well end up breaking a few more.
I seriously doubt that it even works at all. Speculating over whether it can attain light speed seems a bit premature at this stage. But it wouldn't need to reach such speeds to be either (a) useful or (b) a remarkable breakthrough in propulsion.
At this point, as I understand it, the concept is still being actively researched, so maybe in a few years the idea will either finally disappear or finally prove valid, somehow. I can't say I am holding my breath, but we'll see.