Interesting that you say it was not successful in and of itself. It was certainly much tougher and bloodier than Grant wanted (Lee ability to use his available assets saw to that), but think about the definition of success here. Grant wanted one of three outcomes: 1.) Lee fighting in the open and pretty much getting the ANV destroyed; 2.) Lee being cut off from Richmond & supply, leading to the fall of the city and isolation; or 3.) the ANV trapped in a siege at Richmond, inevitably bagging both.
I believe Grant infinitely preferred option 1, but Lee was far too good a general to ever oblige (he was no Hood). Option 2 would help the Lincoln campaign, but leave the ANV as an effective field force - perhaps if supplies or political pressure forced Lee to attack, it might serve the same purpose as option 1, but again I think Lee too competent for that. Option 3 removed the ANV as an effective field force and ensured success over both targets, but would take the longest, be bloodiest, and might be too late to significantly help the Lincoln election. But those were all flexible End Game results for Grant to win the campaign.
For Lee to win the campaign, he would need Grant to fail at all three of the above options, and remain a threat in the field. If he could keep Grant north of the James, or cause Grant to retreat (or even pause in inactivity for a significant time), or (best case) smash a good part of the AOP in a climactic Napoleonic style victory (ala Chancellorsville), its highly likely Lincoln might lose the election.
A true 'draw' would have seen both armies staring out across each other, exhausted but free to move. Lee being trapped in Petersburg was no draw, and Lee knew it and angrily acknowledged it. But it MIGHT be enough, with good press, to fatally hurt Lincoln's reelection bid. In prizefighting terms, Lee was beaten and immobilized into his corner but staying on his feet, crumbling bit by bit, hoping for the bell and a favorable judges' card (the northern voters). Once it went extra rounds, the fight was over ... except for the needless extra punishment both took.
In eight weeks, Grant succeeded at one of his End Game options. Lee did not. I give full props to both men for their skills, uses of advantage and adaptability during the campaign - an incredible tense slugfest by both.