Graham has been used exclusively in a starting role in the minors since 2012 and the Braves could opt to keep him stretched out this season, but based on his stuff and projectability many view him as a future back end reliever.
If Graham throws well in the minors at the early part of the year it is certainly reasonable to expect him to be on the major league roster at some point in 2014. The most likely landing spot for him would be in the bullpen, ala Craig Kimbrel in 2010. The timing could be close to perfect as Kimbrel will be getting even more expensive next season, so if Graham shows his stuff as many expect him to we could be looking at a "closer in waiting" situation.
Now, that is far from a certainty and is also a long ways away. First, we need to see Graham healthy and on the mound. His upper nineties fastball and solid curveball give him that two pitch repertoire that often succeeds in the back end of the bullpen. I understand the Braves willingness to let him start, and it has not yet been announced that that is what they plan to do, but I would expect Graham to land on the major league roster at somewhere near the midpoint of the season either in the rotation or in the bullpen if he stays healthy.