I think officially passing the general pediatric boards is not required to complete the fellowship, but it depends on what your definition of fellowship graduation is, and as a result, what the program director defines as graduation. My program had instituted a rule that passing the general pediatrics boards was required in order to advance to the third year of fellowship. I don't think this is an ACGME mandated thing, and in fact in our case was in response to one fellow having had to take the general boards three times to pass.
It makes sense to not allow one to graduate from fellowship without having passed the general boards, as to be board-eligible for a pediatric subspecialty examination, you must have passed the general pediatrics board exam. It will also be impossible to find any jobs, at least academically. In all job postings it is clear they are looking for "board-eligible or board-certified" pediatric subspecialists, which one cannot be without first passing the general pediatric boards.