Mance's 'king's blood' is shown to have significance in the books at least. Jon sends Mance's baby son away precisely because he was afraid Melisandre would sacrifice him. The perception of Mance's kinghood might be just as important as a noble bloodline, even if it from people in the South and not his own followers
That relies solely on the perception of Mance as a king. There's no actual evidence that his blood would be as effective as a more traditional king, or more effective than a normal person's blood at all.
Lil' Mance wouldn't have carried any inheritance beyond his parenting anyway. He might be considered a prince the same way the southron knights consider Val a princess, but if there's no form of succession do bloodlines even matter?
Stannis had damn well better win his next dozen battles if the idea of sacrificing king's blood is to have any real basis.