it might have stopped the British Empire in its tracks, Clanad? Current thinking seems to be that after the loss of the 13 colonies they realised future colonisation would have to more carefully handled and the colonists given a bigger say (still none for the indigenes, of course). It culminated in New Zealand being taken over only by consent and by treaty with the natives.
My own guess is that actually you American chappies would just have kept on rebelling and won your point later rather than sooner, but who knows?