In 1777, as part of a grand strategy to end the war, the British sent an invasion force from Canada to seal off New England, which the British perceived as the primary source of agitators. In a major case of mis-coordination, the British army in New York City went to Philadelphia which it captured from Washington. The invasion army under Burgoyne waited in vain for reinforcements from New York, and became trapped in northern New York state. It surrendered after the Battle of Saratoga in October 1777
Suppose the British army in New York moved north to meet with Burgoyne's force and took New England for the loyalists. They then turn south and take Philadelphia regardless. What would have happened in such a scenario?