Totally depends how it goes.
It seems unlikely George Washington would be at all remembered by anyone not really into their history so involving that is unlikely.
It also depends what happens afterwards.
Would there be another rebellion so the 'first' qualifier is necessary?
Agreeed with all here. Most likely with an early put down of the rebellion, whether by overwhelming forces sent much earlier pre-1775, OR Total Victory in 1776 (Invasion of Charleston a success, Canada never threatened, Washington's Army destroyed and he and his staff captured). Once France launches its DoW the ARW becomes a world war and the chances of British conquest of the Colonies becomes remote. [1]
1] Though considering Britain's obsession with maintaining the blockade of the Colonies and waging economic warfare against all attempts by the French to materially succor the American Army, to the detriment of defending all parts of the Empire short of Jamaica, Gibraltar, and Britain herself... [2]
2] Though if the French Revolution and Napoleonic Wars are not butterflied, I'd hate to be the British Commander of British North America. This could well mean either "Round Two", or else butterflying the whole Peninsular War in favor of swallowing up the entire French and Spanish Empires overseas (Including the Louisiana Territory?).
Maybe a Napoleonic victory (or at least an end to the wars on terms favorable to the French), thanks to exhaustion of British morale and resources trying to keep the colonies pacified overseas?
Washington's Rebellion.
If the rebellion is put down, I don't think that necessarily means future revolution until successful in the future. What it could mean is an America that goes a bit like South Africa: a colonial area that may commit another rebellion in the future, where you have the American group form an independent identity against (further) British colonists, leading to a dominion that has an independent streak and eventually does gain its independence based on the American vote, possibly with negative racial overtones in regards to the American Indians.
Or the 'American group' is so thoroughly discredited that the colonists try to be so loyalist they are beyond reproach. American would be synonymous with treason, hard to see many people wanting to tar themselves with that brush.
Perhaps this could eventually lead to incorporation and the colonies becoming counties.
Without knowing how the war ends or who is the dominant party in parliament afterwards, it's hard to judge.