You always have a right to appeal. Whether or not you should do so is not clear. If you win, your PD must promote you on schedule, but you can bet that you will be under the microscope and any further problems will be dealt with. If you lose, then it's evidence of your lack of insight.
I think a resident should file a complaint if they believe that they have been judged unfairly, and that should be the sole criteria.
I wouldn't second guess and worry about making anybody more upset as if the resident believes he or she has been unfairly judged/treated then the attendings already don't respect the resident if this is the case.
Losing can all mean all sorts of things in reality, from a lack of insight to the PD exerting pressure on attendings to side with them, to a loss of perspective among attendings and how bad training/environment/malignancy is at a program. At least you know you that you did the right thing.
There are a lot of very malignant personalities in medicine at the attending and PD level, I think people who want power are drawn into academia and faculty positions and lack perspective when getting into personal conflicts with subordinates.
I have seen some *amazing* conflicts among people at the dean's level with department heads and they fight quite literally like school children! And sure, I have seen it lead to a department chair being fired! This is the "politics" of medicine at some, but not all places, at the nice places everybody really respects each other and such conflicts are unhead of. Mostly I would say the Northeast has this problem, but I have seen it everywhere, and it is sad. I once was on a service where the attending we were working with was harrassed daily by a department chair who came down and yelled at him in front of everybody, everyone knew he was very good clinically and patients loved him and the department chair was from Mars. Knowing this, and how destructive such fights are at that level, they are very lopsided and worse at the PD vs. resident level.
This is what really S&@#$ about medicine in general in that in other fields, yes, you will have a more collegial relationship with your colleagues.
Abraham Lincoln sad that basically the best test of person isn't putting them into adverse circumstances as many of us can survive adversity, but to give a person power . . . and see how they survive that. Power corrupts and when you a person who has been PD for a long amount of time, sure, they probably lose a good deal of their perspective and letting someone pass is more a personal seal of their approval based on gut feelings and subjective evaluations of the person's character not based on their work performance.