While it is impossible to say with any certainty whether any set of historical facts happened “inevitably,” it does seem highly unlikely that Europeans and Indians would have, under any circumstances, been able to fully cooperate. The very fact that the natives living in the Americas were referred to as “Indians” – and the fact that the name stuck- is evidence of the euro-centric worldview which dominated all contact between Europeans and Native Americans. The economic, political and socio-cultural motives that drove the first European explorers and settlers to establish themselves in the Americas placed them entirely at odds with the natives. Europeans were driven by profit and empire, as well as by the drive to spread Christianity to the heathens (as they saw them) in the Americas.
For evidence of this, a look at the history of other regions colonized by Europeans tells the same story. The continent of North America may have been different than the parts of Asia and Africa that were being colonized, both in terms of the people that were living there and their isolation from the trade routes of other parts of the globe, but the results were the same. Once Europeans established themselves there they began to exploit the local resources and populations for the benefit of Europe. In that context, then, it is doubtful that “full cooperation” was likely, or even possible.