The Yankees struggled against lefties in 2013. As a group, the team had a below-average 84 wRC+ against southpaws and no member of the Yankee bench was really that great against them. Their right-handed batt off the bench, Vernon Wells, only mustered an 89 wRC+. If the Yankees want someone who can hit lefties off the bench, they could recruit Reed Johnson for their cause.
The Braves just bought Johnson out of his 2014 contract, so he's hit the open market. He hasn't had an above-average season since 2008, but in his career he doe have a 118 wRC+ against lefties. He didn't hit them well this past season, but he's been solid throughout his career. While he would only be asked to play against lefties, his career 84 wRC+ against righties (124 wRC+ in 2011) suggest that he's at least not completely useless against righties in a pinch.
Johnson wouldn't make much of a defensive replacement since he he's hovered just under average for most of his career. He hasn't even been a good baserunner based on his negative base running rates and lack of stolen bases every season. His bat against lefties would really be his only strength.
Obviously, the Yankees would have to cut Wells, which wouldn't be a big loss, but they'd still be on the hook for the $2.5 million they owe him in 2014. He made $1.5 million in 2013, so replacing Wells with Johnson would cost around $4 million total. It wouldn't make sense to have Johnson and Wells on the team. The only way replacing one with the other would be worth the cost is if they don't plan on replacing Curtis Granderson with someone like Shin-Soo Choo or Jacoby Ellsbury or really anyone at all. If they go the 2013 offseason route again, then Johnson would make perfect sense. Unfortunately, that means that nothing good will be happening for the Yankees either.