Yes, Anaconda worked.
But only because of the continued, and expanded, political will in the North to win.
Recall, for instance, that during the Battle of Gettysburg there were major draft riots in New York. And Lincoln had the Copperheads to contend with.
Had Lee won at Gettysburg, or avoided it entirely and successfully moved on Harrisburg and/or defeated the Army of the Potomac in detail, the pressure on Lincoln to negotiate a settlement would have been enormous. Had the 1864 election taken place with either a stalemate or the Union armies attrited (as opposed to maneuvering ever-forward as the twin victories at Gettysburg and Vicksburg enabled), Lincoln probably would have lost to Little Mac, who would have negotiated a settlement.
As I said the Union could have stopped but the Confederacy from a purely military view had NO path to victory.
The Confederacy had to hope the same strategy that worked for Washington in the reveloption would work for them, it did not in large part because the distance issue (no atlantic ocean to contend with) and no allies that were willing to aid in the fight (the French, esp the French Navy)