"Theoretically, an egalitarian society would be one in which every individual is of equal status, a society in which no one outranks anyone. But even the most primitive societies could not be described as egalitarian in this sense" (Sahlins 1954)

In the sense of absolutism, no, were no truly egalitarian hunter-gather societies. However, it is important to remember that social systems (like all things human) lie on a continuum. On one end, there are total egalitarian societies. On the other end, there are highly stratified state-level societies. I think your question(s) cross back and forth between the amount of social stratification and social hierarchies; both of which play into what might make a society egalitarian or not. First, social stratification refers to the division of society into institutionalized ranked categories into which people are born. This rank is inherited, not achieved. These categories endow all their members, irrespective of sex or age, with the privileges afforded by their rank. The archaeological record does not show evidence that this was the case for hunter-gatherer societies. You are correct in saying that there was no real wealth or real notion of property (relatively) and, thus, no real power to leverage over others. This is not just speculation, though. There is loads of archaeological evidence from burials, excavations at campsites, etc...that people did not have much of what we would consider material wealth. It would be difficult for hunter-gatherers, being highly mobile, to move around on the landscape if they were packing around a lot of (probably) useless stuff.

With regards to your question about the arguments about men being dominant over women, competition for food, etc...For the first argument (men dominant over women), there is quite a bit of ethnographic evidence that women ran the show in many small hunter-gatherer groups. These groups tended to be matriarchal. Regardless, there does not seem to be much evidence that there was too much gender inequality one way or the other. For the second argument (competition over food), intra-group competition was likely incredibly rare. Hunter-gatherer groups were small and likely related to each other. Being related to most members of your social group would really cut down on the competition for food. Inter-group competition for resources also seems to be rare. There is little archaeological evidence for inter-group violence among hunter-gatherers. There was some, to be sure, but it seems very limited. Groups likely knew where other groups were hanging out and, thus, avoided those areas as they would be low on food resources anyway. As for fighting over lands, again, there is very little evidence from hunter-gatherer archaeology for conflict between groups. Archaeologists really don't start to see conflict in the record until the transition to more farming based societies, when the notion of 'this is my field, stay out' and property began to pop up. Institutionalized warfare over land does not appear until the appearance of state-level societies. Think of Uruk and Ur.

Second, social hierarchies refer to the interpersonal relationships. Inequalities may exist, even in hunter-gather societies, with regards to social hierarchies. This is where gender inequality would come in. I don't have much background in this area of social anthropology, as my specialty is archaeology and anthropology, so I won't try to explain this.

Hope this helps! Let me know if you have any questions or need clarification.