The theory is hardly plausible because i dont see Tsunade giving up her love child with Dan[for adoption], after it was shown how devoted to him she was.
I find it highly unlikely that she would still forfeit looking after Naruto if she truly is Naruto'd granny. There might be a relation because of the Senju blood that most likely runs through both their veins but i think you're aiming too high to tie up loose ends.
Tsunade is definitely not Naruto's biological grammy, probably they are of distant relation from what has been said about the Senju and Uzumaki, and i am sure of this because Namikaze is almost definitely Senju[still not confirmed] and Kushina is a confirmed Uzumaki and it showed the partnership that had begun with the 1st and his wife. And if i may ask, y not show the 4th as one of the people that Tsunade has lost if she really was the mother? Don't you find that as shoddy story telling from Kishi if that were to be the case? I would understand trying to build up the suspense but that seems too far-fetched...