The national territory you described is a LOT of land, which would have to be defended by a relatively small number of Iroquois from land hungry settlers from England. In addition, they would have to fight other tribes for territory.
The Iroquois were relatively well organized, and with a mixture of luck and a genius military leader could carve out a territorial base. If France does not lose their colonies, and the Iroquois play their cards exactly right, maintaining peace within the confederacy and using their Indian and European enemies against each-other, they could get a land grant to serve as a buffer between the French and English colonies. It's doubtful that the confederacy as a whole would be given enough land to support their traditional lifestyle, which is partly hunting dependent. So, you'd either get an Iroquois nation which is inhabited by only a fraction of Iroquois, or a single Iroquois nation which suffers from overcrowding and the environmental and sociological degradation that comes with it.
Even this scenario requires an insane amount of luck over a very long period of time. It would make an interesting TL, but there's a reason why this didn't happen IOTL.