The answer is no, and the team needs to sell it's remaining assets. Fangraphs playoff odds has us at a 10% chance to make the playoffs, which is the highest it's been in weeks. The team has realistically no shot and has been riding a streak of unusually hot pitching to this winning streak.
The streak is unfortunate because it has probably lowered Hal Steinbrenner's chances of allowing Cash to sell Miller/Beltran/Nova/Pineda/Gardner for any prospects at all. Especially Miller, who after the amazing haul we brought in for Chapman, would only bring more.