Conor Friedersdorf thinks so, in a pretty perspicacious piece at the Atlantic. Highlights, after surveying the quality of LP candidates dating back to John Hospers in 1972 (the only one to win an electoral vote, thanks to renegade elector Roger MacBride, who became the LP's 1976 standardbearer):
A former governor of New Mexico, he was re-elected by that state's voters, left office popular after two terms, and therefore has the most executive experience of any Libertarian Party presidential nominee. He can also cite the state he ran as evidence that nothing radical happens when he's put in charge. An economic conservative and social liberal, he represents a new direction for a party that has long wrestled with its paleo-libertarian wing. And yet he too is certain to lose on Election Day, as third-party candidates in American presidential elections do. The question is whether he can match his party's 1980 high-water mark and win 1 percent or more of the vote, and whether he might win even more in the key swing state of New Mexico, where voters already know and have cast ballots for him.
Reason's coverage of the LP convention this past weekend in which Johnson won the Party's nomination.
For much more on the history of the LP, see my book Radicals for Capitalism: A Freewheeling History of the Modern American Libertarian Movement.