Does a Junta during the Cuban Missile Crisis end the game?
does that trigger the end of the game clause on the Cuban Missile
  Crisis?


Yes. From the rulebook:


  6.3.5 Cards that state a player may make a “free Coup roll” in a particular region may ignore the geographic restrictions of the current DEFCON level (see 8.1.5). However, a “free Coup roll” used against a Battleground country would still lower DEFCON as per 6.3.4.


A free coup attempt event only negates the geographic location, not DEFCON status. This would still cause DEFCON to reach 1 and the phasing player would still lose the game after attempting the coup.