I think he’s there to set up internal conflict in the North. 

If Wyman Manderly believes Rickon Stark to be the last living legitimate son of Ned Stark, you’d better believe he’s a true contender for the Northern throne. I imagine there’s going to be not a few people who’ll argue that Robb wrote his will believing Rickon to be dead, so that invalidates the will. 

Likewise, I’m sure the forces of the Vale will argue that Sansa is the last legitimate child of Ned Stark, and that Rickon is an imposter pretending to be a dead prince. In rebuttal, I wouldn’t be surprised if the Manderlys argue that Sansa is an imposter put up by the treacherous Littlefinger and that sons come before daughters.

Similarly, in Jon Snow’s camp, there will no doubt be arguments from the Glovers, Mormonts, and Reeds that the will should trump all, that an adult male proven warrior is a better choice than a child or a woman. (On the other hand, when R+L=J comes out, that’s going to complicate the situation, because bastard-born or not, Jon Snow comes from the female and not male line of the Starks.)