Yes, the killscreen is technically possible to complete, however it's too unlikely to ever happen in a real game.

I don't see why the RNG wouldn't be controllable enough to do this. Every frame you have 3 possible inputs that you can give: either left, right, or nothing. Each choice will result in a different sequence of random numbers, and not only that, but due to the nature of the DK random number generator the three possible sequences very quickly diverge to become totally independent of each other. This is just with a single frame, now if we look at say, 10 frames, with 3 possible inputs on each frame we get 3^10 = 59049 possible sequences of random numbers, which seems like more than enough to be able to find one that allows getting a 0 least significant bit for 5 consecutive frames.