(One-time Ascent veteran)
I think walking is a very important part of training. It would be ideal to train by walking up steep hills, but flat walking will still help. Walking emphasizes some different muscles than running, and you want those muscles to be in top shape. As you train, keep an emphasis on learning how to walk *fast*. The more you practice, the more efficient you will become and your pace will pick up. Be careful at first b/c your shins might feel sore - build up to it. Also learn to really use your arms to propel you forward. Finally, a good skill for mountain running is learning to transition back and forth between walking and running. Runners usually think of walking as "taking a break". In the mountains, its more a matter of "How can I move forward (i.e., up) the fastest ?"