Will Jon go beyond the wall to save Bran?

[The Commentator]

10 hours ago, broken one said:

I doubt Bran ever leaves the cave in his own body. His mission is for a lifetime (expanded lifetime). Sam will not spill the beans and so no one will know, except for him and Reeds.

He could change his mind after he learns what happened to Jon at the wall.  BR will try to stop him and that is where master and student may pick different roads.

[BalerionTheCat]

1 hour ago, Widowmaker 811 said:

He could change his mind after he learns what happened to Jon at the wall.  BR will try to stop him and that is where master and student may pick different roads.

I have more faith, hope, in BR and Bran to help Jon, than I have in Melissandre. But to be of use they need the cave, where to power of the Old Gods reside. The only place they're useful.

[GoldenGail3]

But he doesn’t know that Bran is still alive though..

[Bloodraven’s Spider]

Jon will not head north of the wall to save Bran. First Jon has to learn Bran is alive and north of wall, where and how is he going to learn this information? And not t mention he needs to be brought back to life or warg back to his body from ghost depending on what you believe. 

All that has to happen and Ramsey needs to be settled with (Jon will not go north or south until Ramsey is defeated, maybe Stannis takes care of that) but he will need to then lead a group north, during winter and with the WW/Others nearby. Bran will either be trapped in the cave (i dont believe he will be) or will leave eventually and have help from COTF/Coldhands. Jon will not bring him back from the cave.