Long story short: not going to happen. Aside from having no strategic reason to join the Revolution, we have genuine examples from history of how the situation would go.
The Lenape tribe split, with one of its leaders, White Eyes, signing the treaty of Fort Pitt, which guaranteed land and mutual alliance between the Lenape and the fledgling US in exchange for material and intelligence support in the Great Lakes. You want to know how that turned out?
Militiamen whose families lived near the land promised to the Lenape murdered White Eyes during a scouting mission and pretended the British did it. Immediately, backpedaling started on the treaty and more of the Lenape understandably ended up defecting to the British-allied portion of the tribe, which was later seized on as another excuse to take the land.
Alternatively, look at the expansion of settlement in western Georgia and the deep south. When the federal government forbid expansion, settlers moved in anyway, created "independent" republics and then petitioned Georgia to annex them as "protection", coincidentally in territories claimed by Georgia that treaties had reserved for neutral and friendly tribes.
The Iroquois joining would most likely just be one more datapoint in the trend, sadly.