Vice presidential candidates seldom brings their home states on their own (there's usually some favorite son effect, but it's around a couple of percents).
Without a doubt, Kennedy wouldn't have carried Texas in 1960 without LBJ on the ticket. Humphrey wouldn't have carried Maine without Muskie in 1980, since Maine was then a solidly Republican state.
Quayle had some effect in retaining Indiana in such a wild year as 1992, but we can't rule out it would have went to Bush anyway. The same for Gore in 1992 and 1996.
1992 and 1996 with Al Gore and TN.
If Gore delivered TN in 92 and 96, why couldn't he deliver it in 2000 lol?
Tennessee had underwent a huge political changes between 1992 and 2000, becoming more and more Republican. It was close in both 92 and 96 so we can reasonably assume Gore's presence did make a difference. Whether enough for Clinton to carry the state, it's debatable.
However, Gore could've easily carried his home state in 2000, given how close it was (and it wouldn't be as close had Gore been from somewhere else). All he had to do is to actually campaign there a little.