No, the Democratic Senate majority does not hinge on Mary Landrieu.
Of all the Democrats running, Landrieu’s race may be the most important. In many ways, she’s a keystone. It’s hard to see Democrats holding the Senate if she loses, but it’s also hard to see them losing the Senate if she wins.
It's hard to see Democrats holding the Senate if she loses?
Republicans need to pick up six seats. Of the endangered Democratic incumbents, Landrieu currently sports the worst numbers.
So it's very easy to see a scenario where Landrieu loses and the Democrats hold the Senate by winning every other contested seat. It's called "a smaller Democratic majority", but a majority nonetheless. So no, it's not the most important race of the cycle, and won't be unless it heads into a December runoff with Republicans already having picked off five seats.