I like to think that Bran will learn to talk through the trees at some point and become the 'Voice' of the Old Gods. However, if that happens, I don't believe he'll help Stannis.
Stannis is a (false-)champion of
Fire....don't we need a champion of
Ice, to balance it out? Would make sense, yeah?
Ultimately, the
true champion of Ice might be the Great Other, but I see the analogy of
Fire and Ice as being valid on more than one level (as in the human and religious level, the supernatural level and the 'natural' level as in Winter/Summer or North/South etc.) thus allowing, for more than one 'champion'.
The fire and ice dichotomy is also the reason I strongly believe that if Jon survives or is resurrected, Melisandre will have little, if anything to do with it. We've already had Cat resurrected with the power of R'hllor. Actually, we've had Dany, surviving the fire through a freak accident, with the power of R'hllor. We have Victarion, championing R'hllor... isn't it time to see a bit of the old magic? the kind that holds the wall together? The kind, wildlings might know of?
I think it more likely for Bran to become Melisandre's counterpart, representing the Old Gods of the North and to chose a champion of his own to back up.
He might be known later as Brandon the 'Tree Talker' or the 'King Maker' or 'Thousand-eyed Bran' ... or he might lead an army of wolves. Brandon Thousand-Skins?

remember Nymeria is still prowling out there with her pack, and Arya is conveniently absent. I think... Nymeria could find a new master in Bran.
And by the way... If Bran ever did leave his tree and met up with other wargs... wouldn't they hate him? consider him a freak for warging Hodor? Varamyr himself didn't seem a man with much honor, but even he thinks to himself that it's a crime to warg another human being.