I dont really believe this theory but with that being said I see it as a definite possibility so I feel the need to explain my arguments against some of the statements a few of you have made:
1. Age...tsunade being around 54 and naruto being around 16 does make the age difference between them, well...cutting it a little close, I mean since its a family oriented manga I can't see Kishi writing tsunade had gotten pregnant too young...but if minato is 36 (if he were alive) that would mean tsunade got pregnant at 18, so that is still too young but it would be deemed as fairly acceptable.
2. Your argument that the third hokage was not a senju is rather pointless to be honest, because it is obvious the 1st and 2nd thought of him as family and would therefore allow it anyway.
3. I could DEFINETLY see Kishi keeping this a secret for so long, totally blindsiding us with the idea that tsunade is narutos grandmama...so no I don't think if this were the case we would have read about it already.
Tsunade and Naruto have a strong family resemblance when it comes to personality, the reasons are obvious...hot tempered, knuckleheaded and all that, it makes perfect sense to me. Also I could see Tsunade leaving the village and making Jiraiya promise to take care of Minato. With all this being said I still greatly doubt this theory and will be doing more research on it so I can post my own thread stating where I stand on this theory in the future.