I'm guessing once you get there, controlled deceleration and getting into an orbit might be a bit of a problem at that speed. If there are enough particles for the nukes to keep pushing the rocket along, the fact that they are extremely sparse isn't going to evade the extraordinary level of heat generated from the friction, and there would be lots of gamma rays (and more) from particle collisions at the leading edges of the rocket. Also, if you hit even a spec of dust on the way, it would obliterate the mission in a spectacular way.

Matter travelling anywhere near the speed of light has a lot to contend with.