So even in the DES hash, it's possible you'd have to perform 64^8 = 281,474,976,710,656 cycles before you can satisfy the equation.
It's possible, but that too is highly unlikely.. mainly because it implies that all hashes chain together perfectly to form a single period-64^8 cycle. at most (?) the longest cycle (at random) should probably be at least a binary order of magnitude less... probably closer related to the longest run over n random bits ;D
is dependent on how many collisions the function has.
i'd also argue that it has more to do with the number of disjoint cycles than collisions =)