I have less experience, but this matches what I saw and experienced in cross country exactly.

My starting point: couldn't run a quarter mile. After a few years: 6:30 mile, didn't have much trouble with a 12 mile run.

I basically would be extremely surprised if a serious exercise program didn't improve performance. The only caveat is if we're talking about someone who can't run, due to bad knees or something. I've known people like that and I don't know how to get around it safely.