Sadly, I believe that things would have ended up pretty much as they did. If the Europeans did not do it, someone eventually would have. The resource rich nature of this continent and overpopulation of the rest of the world would have insured invasion.
Native Americans did not have a reason for developing military technology because they never overpopulated this continent, which is, in my opinion, one of the main reasons for serious conflict. Even if they had reached that point and developed equivalent military technology, they would still have been screwed:
Nothing would have prevented the plagues any invasion would have brought. In my enjoyment of thinking of alternate history, I like to theorize about what would have happened had the Native Americans been resistant to disease.
Yes, I think they would have lost due to aforementioned resource rich continent and greedy invaders, however, they would have taken an even greater chunk out of the invaders. Even with the plagues and lesser military technology, they kicked butt.