The way I see it, Cochran wasn't going to win anyway. He can't win challenges, and once the other tribe was gone, he would've been picked off right away by his own tribe, because in that scenario they wouldn't want him in the Top 3 for fear of receiving "underdog" votes.
So now, he might actually proceed further and get to the Top 3 because everyone knows he won't get the votes to win after pissing off his former tribe. So in that sense, he's going to last longer in the game.
I agree. I think it was a bold move and hopefully it will get him further.