Totally depends on the course. FWIW - I don't run, but I race 'cross reasonably well. Most courses will only require SHORT runs, typically up hill and over barriers. Anyone can accomplish this.

My DH is also a non runner, and is competitive in the Elite and Elite Master's fields.

This past weekend, we raced on a course with one/two run-ups (I couldn't ride the second hill, but many could). The runs were pretty short. Last weekend, I raced two different courses - one with VERY little running, and one with only one running section (over the barriers). Next weekend we will be racing in RI, where there are TWO LONG beach runs. Everyone, runners and non, gets through it.

The short of it is, if you have power and good bike handling skills, running (or not running) will not be a hindrance to you.

Have fun! Cross is such a blast.

SheFly