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Are you breathing hard? Is your pulse rate elevated? Are you maintaining that level of exertion for a fairly lengthy time (more than twenty minutes or so). If your answers are "yes." you are essentially doing aerobic activity and with time you will be stronger and faster.
I used to run a good bit, 70 or more miles a week, especially when training for marathons, and i found that i could hike longer hills and steeper hills, with no muscle fatigue or cramping, and a lower pulse rate,etc., so running improves hiking. I think it works both ways.