Was Gettysburg that decisive compared to other battles? Had the South won that battle, it doesn’t change the outcome of Vicksburg, the defeats in Eastern Tennessee, Atlanta and the March to the Sea.
All that does not matter. If Lee defeats the army of the Patomac then nothing stands between Lee and Washington but some garrison troops. Lincoln probably asks for an armistice.
Not a chance Lee takes or even pressures Washington into armistice. Even if Lee wins the Battle his Army takes huge casualties and is in no shape to take Washington. It took Grant 9 months to take Petersburg, and Grant had resources Lee could never muster. Garrison troops would have been manning positions that were in place for months.