Like I said I'm not a runner, but in fair shape (sometimes). Last year I did the crossing in like 7:15 or something. My fastest by a good hour. I went North to South that time as well, running (more like jogging) all the downhills along the way and hiking any uphills. I even used trekking poles while running downhill.
I would imagine if your going for 5 hours then your a true runner. The only think I would add that you would want to bring is more water and more food and electrolytes than you would think you need. My friend passed out. had some convulsions, throwing up last year from hyponutremia (sp), he's ran a few marathons, the crown king scramble, a 50k and a 50 miler and still underestimated the salts/electrolytes he would need. We was on pace for a 5 hour trip I believe. Hit the wall hard about 2 miles from the top.
As long as you plan it for when the North Rim still has water running, that shouldn't be a problem, plenty of water along the way. I think the longest stretch w/o would be 7 miles.