So if Davos brings Rickon back in one piece, then am I correct in assuming that he now has the true heir to Winterfell? (Can’t Imagine Bran ever returning to the normal world.) This could pretty much ruin almost all of Littlefinger’s plans involving Sansa, no?

Well, here’s the thing, I think there’s going to be a good deal of conflict, or at least potentially: 

1. Rickon will no doubt have the support of the Manderlys and probably Stannis too, but other people might be resistant to giving the southerners that much power, especially if Rickon is hastily betrothed to a female Manderly (Manderly is a loyal northman, but he’s also a loyal northman who makes sure he gets rewarded in full). 
2. Sansa is older, and is being championed by the Vale. OTHO, she was married to Tyrion Lannister before, and the North isn’t going to like that her first husband might try to assert a claim. 
3. Robb’s will naming the significantly older Jon Snow as his heir may be championed by the Glovers, Mormonts, and Reeds.
4. The Liddles and the other hill clans might back Bran Stark, who they know is alive and the older of the surviving trueborn sons.