Agree with what j4pac mentioned above. The association between "chief" and "competitiveness for fellowship" is mostly correlative and not causative. If your goal is to get a pain fellowship, you should not necessarily be gunning to be chief. Believe me, there are better things you can be doing with your time than fretting about being chief and actually being a chief. Think of being chief as a hobby, not a chore towards fellowship. If you find yourself a generally responsible person, hard worker, legitimately respected by your peers and superiors, have a thick skin, don't mind hearing the complaints of peers and superiors, and being very political, then you're probably cut out to be a good chief. And some people legitimately enjoy this.
But if you don't think you would be good at this, don't sweat it you can still land very competitive fellowships. In the end, yes being chief may help in fellowship competitiveness in so far as a program director may see chief resident and think "probably a good, responsible, hard working, and well respected guy/gal." But if your recommendation letters and your interview don't reflect this, it doesn't matter if you were chief or not, you won't be ranked highly. On the other hand, if you're not a chief and your recommendation letters and your interview reflect you as a "good, responsible, hard working, and well respected guy/gal" then you'll be fine.