I remember seeing this scenario before. My understanding was that Custer's success was seen mainly as a good example of how effective the new Spencer repeating carbines, which he was equipped with, actually were.
One other book I saw it in was a collection of scenarios where the South wins at Gettysburg. The upshot, after 7 or 8 other versions of how Lee could have won, was that it would have made little difference anyway, because he still would have had to face an even bigger Army around Washington, and this when cut off from supplies, depleted by Gettysburg and deep in enemy territory.
That is assuming he attacked Washington, it might have been a different thing if he went to New York.