No. The only thing that would have helped is if Gore wasn't Gore.
This is correct.
Gore could've won the election easily, regardless of a running-mate (Shaheen, Lieberman, Kerry, Graham, Edwards... take your damn pick) if he had utterly diffrent campaign. Even with his piss-poor campaign, he still came within the inches, so imagine his results without said bagage.
All true, but Shaheen would still have been a better pick than Lieberman and could have delivered the crucial votes in New Hampshire. So I think the answer is Yes.