You may look for an answer in some anthropological works about hunter-gatherers, e.g. Christopher Boehm's Hierachy in the Forest. Basically, he describes what he calls a "reverse dominance pyramid", which can be observed in many hunter-gatherer tribes. Individuals who are aggressive, bossy, try to behave like alpha-males are mocked, then warned, shunned, and finally killed or left alone when the tribe moves forward (which also ends with death).
James Woodburn (Egalitarian Societies, James Woodburn, Man, New Series, Vol. 17, No. 3. (Sep., 1982), pp. 431-451. here it is) concludes that all of such societies/tribes are profoundly egalitarian and relationships between people are based on sharing, without any long-term dependencies. All distinctions – of wealth, power and status – are systematically eliminated.
This could lead to the following answer: there are non-hierarchical cultures, but they are limited to hunter-gatherers. All known human sedentary cultures are hierarchical and there is some leadership in them, as far as I know.
Your question is also problematic, for two reasons. First, leadership and hierarchy are necessarily the same - we can easily imagine human groups in which we can have a voluntary leadership, but which is only ad-hoc and does not depend on any permanent hierarchy. Second, the phrase "culture depending on the concept of x" can also be read in many ways. Your question does not contain it, but the unproven statement that you propose at the beginning does. So be careful in proceeding from an answer to the question to the validation of this statement. You must add something to the mere observation that all cultures have an element of hierarchy in order to establish a fact that they depend on it - we might just observe such correlation in the world. Maybe they were some selection pressures at work at some moment during the last 10k years (warfare?).