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.