"He ran and went up."
Its actually means: 他跑了 emphasize that "he ran" as an action to reach "up".
You are partially right about "ahead of us" because the speaker should be standing before "he" who ran up to say like this. But it's not always accurate to think that this sentence imply the person is ahead of him. It simply say that "he" use run, not walk or climb, as an action to reach the "up"