The answer is no, for a variety of reasons, the most important of which being the fact that "Native American societies" is not a homogeneous group. There was as much, if not more, variety in social organization among Native American societies in the 15th century as there was in Europe. Additionally, there was a lot of variation over time: just as the social organization of European societies changed over centuries, the social organization of different Native societies changed significantly over the 12,000+ years of human occupation in the Americas.

To answer the question more specifically, were there, at some point in time, any Native American societies that could be examples of "proto-Communism"?

Let's start with what it means to have a "proto-Communist" society. Minimally we are talking about a non-hierarchical society in which the means of production are available to ever member. A lot of the blame for ruining alleged "proto-Communism" is thrust on the transition from hunter-gatherer lifestyles to agricultural lifestyles at the beginning of the Holocene. Agriculture in this view is the beginning of private property and surplus production: the eventual root of primitive and capitalist accumulation, a la Marx in Capital. This is also the root of "class society", e.g. hierarchical society.

A lot of that blame is more or less in line with archaeological understanding of the transition to agriculture (though I should again stress the variability present in early agricultural societies).

This is the first strike against proto-Communist Native American societies, in that the vast majority (in North America at least) lived in sedentary agricultural societies for the last 2000-3000 years. This includes the majority of the East coast, from northern Florida up to New York/Ontario, and west to the Mississippi, as well as most of Arizona and New Mexico, and parts of northern Mexico and southern Utah/Colorado. Some areas of the Great Plains (particularly along the Nebraska river) were dominated by semi-agricultural and agricultural societies. Not to mention the majority of Mesoamerica, which is a part of North America even if it tends to be ignored as such. On that basis alone we can rule out a huge chunk of the continent for thousands of years.

The remaining, non-agricultural societies would perhaps qualify as "proto-Communist", but we run up against another stumbling block in that modern archaeology has recognized that agriculture isn't the only "mode of production" (to stick with our Marxist theme) that produces surplus and hierarchical organization. Some of the best examples of this, in fact, come from North America. The Calusa in southern Florida (and their predecessors), many of the Native American groups living along the California coast, and many of the societies inhabiting the Pacific Northwest all had fairly complex societies (complex in the sense of having distinct social roles), surplus production, and some degree of hierarchy, but none relied on agriculture for subsistence. In each case, highly abundant marine resources played a huge role in allowing for surplus production, as well as the general abundance of other resources in their environments.

What I'm getting at is that the idea of North America being populated by small, egalitarian bands of hunter-gatherers (the romantic ideal behind ideas of Native America as "proto-Communist") is a huge misconception, especially for the last 2000 years or so. There certainly were small, egalitarian bands of hunter-gatherers that might have organized themselves along the lines of something we could call "proto-Communism", but they were not the majority by far. Indeed, you can find examples of this kind of social organization on every continent nearly up until the present (and indeed into the present in many places). This kind of social organization isn't unique to Native American societies, nor is it especially more characteristic of Native American societies than societies on any of the other continents.

Hope that helps.

Edit: Typos and clarification.