Yes, Johnson has a shot, albeit a very small one. I am in no way going to predict the outcome of elections. So much can happen between now and then to affect voters. That's why we can't discount any candidates at this time. Even if it's a small possibility, there is a chance that Johnson can win.
It is entirely possible that Johnson could at least make a strong showing at the polls. Many people distrust Clinton and do not wish a repeat of the previous Clinton administration. Many are unsure of Trump's ability to handle foreign affairs. These factors, and others, could very well cause many Americans to consider an alternative candidate who might not have done so otherwise. People have grown tired of one terrible presidency after another supported by the Democratic or Republican Party. Many feel that it is time for a change, a change which will not come under these two parties. They feel that perhaps the time has come for a new approach. This may lead to an unprecedented shift to the Libertarian candidate on election day.
While party names have not changed that often, the ideological makeup of American politics have shifted strongly many times. In all cases, the shift happened when the pressure for change from the public was strong, but "common sense" said that change was impossible because of a hegemony. The results of these two factors is that most people believe that change will not happen until suddenly the tipping point is passed and change catches most by surprise. The destruction of the Whig party was like this, the reformation of progressivism from the Republicans to the Democrats via the Bull Moose Party fracture, and JFK's outshining Nixon in televised debates were all surprises that only weeks before the actual event were thought impossible.
No candidate from the Libertarian party stands a chance at winning the Presidency. This is because of the Republican and Democratic parties. They majority of people will support the candidate from one of these two parties, whether they really like them or not. Any other candidate must climb mountains to even come close.
Because the Republican Party has an unusually terrible candidate in the form of Donald Trump, the Libertarian party might be hoping to be unusually competitive in this year's Presidential race. But while Gary Johnson might be able to peel off enough voters who would otherwise vote Republican to do unusually well, not enough voters share his values or even know about him, and he doesn't have the numbers he needs to get elected.