All things are possible and that is why you run the race. Unfortunately, the odds of Bernie Sanders overtaking Hillary Clinton of the Democrat party nomination are slightly higher than a third party candidate acquiring two-hundred seventy electoral votes and defeating both Donald Trump and Hillary Clinton (or Bernie Sanders).
Teddy Roosevelt was one of the greatest presidents in the history of the United States. After choosing to yield to William Howard Taft in 1908 by not running for re-election, then disappointed in Mr. Taft, created the Bull-Moose party in 1912 attempting to regain the White House. The result was splitting the Republican vote between Roosevelt and Taft allowing Woodrow Wilson (D) to have a plurality of the popular vote and the required number of electoral votes in the then forty-eight state union to become president. Seems to me if Teddy couldn’t do it, nobody can.
Continuing on that train of thought with respect to the Electoral College, even if this third party does endear enough voters disgusted with both Hillary Clinton and Donald Trump and actually win a majority of the popular vote, it is the electoral vote tally that counts. As rare as it is for a U.S. president to get elected without winning the popular vote, it has happened. Examples include John Quincy Adams, Rutherford B. Hayes (his fraudulency), Benjamin Harrison, and George W. Bush. If the bible-belt and Dixie are going to go predictably red while California and the northeast predictably blue, that leaves a small number of states with a small electorate where the third party candidate has a slim chance of winning a majority and picking up the EVs; two-hundred seventy is still not practical.
The only back door to a third party winning the presidency under the current system is for the third party candidate to pick up some electoral votes and prevent either Mr. Trump or Mrs. Clinton from achieving two-hundred seventy sending the election to the House of Representatives. Only once in the history of this country has the HR selected a president and that was a different set of circumstances. In 1800, Democratic-Republican candidates Thomas Jefferson and Aaron Burr defeated Federalist candidate John Adams and a few also ran. Back then, there was no ticket with a president and vice president and the vice presidency went to the candidate who finished in second place (John Adams, the second president served as George Washington’s VP and Thomas Jefferson, the third president served under John Adams). The HR needed to break a deadlock to determine between Jefferson and Burr who would be president and who would be vice president; of course it was Jefferson. The HR has never selected a president across party lines in the nation’s history. In addition, if it were to happen that way, it would be postponed until after January 3rd when the new congress is sworn in and the new HR would be selecting. If the Democrats regain control of the House, it will most-likely go to Hillary Clinton albeit it is not the best of four-hundred thirty-five, but each state must agree on one vote for the best of fifty states. The Republicans would have to keep control of the House and there would have to be enough anti-Trump Republican congressmen and moreover, enough anti-Trump red states involved in the process. I won’t say your chances of winning Powerball are better, but your chances of betting on the horse with the worst odds, i.e. the greatest long-shot, in the fifth at Belmont are greater than betting on this scenario and betting on a third-party president sworn in on January 20, 2017.