Counting undervotes isn't my theory. It was Gore's theory of which votes should be counted. Gore never argued overvotes--where a voter had marked multiple candidates--should be counted. The recount studies show that Gore would have lost under the only recount approach the Gore campaign actually pursued.
Of course, the whole thing was completely stupid. They should have stopped with the second machine recount. It was completely insane to entertain the idea that you should try and guess what voters meant when they didn't completely punch a ballot, or punched more than one candidate. The proper thing to do is exclude all ballots where the voter failed to fill out the ballot properly.
So it seems like he won the votes anyways. If your retort is "not if we count undervotes, while ignoring overvotes", that would be a different discussion altogether.
The studies showed that Gore only would have won if counting over votes, which his team never pursued: “The studies also show that Gore likely would have won a statewide recount of all undervotes and overvotes, which are ballots that included multiple votes for president and were thus not counted at all. However, his legal team never pursued this action.”
Maybe if Gore had asked for a statewide hand recount the result would have been different. But instead he tried to stochastically cheat through selective recounts, which burned a huge amount of time on a process that was fundamentally unsound.