one of the greatest mysteries that still puzzles me to this day is the seal Tsunade made when Madara was about to attack them again with his Perfect Susanoo.. tsunade seems to be prepared to counter the attack with some jutsu.. see this image:
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i don't what happened later on but this gesture was since then forgotten..
Now, can she have Sage Mode herself? Well seeing Shikkotsu Forest is equally famous as Mount Myōboku and Ryūchi Cave, where Senjutsu can be learned.. the possibilities are quite high.. Now, many were asking why she hasn't used it against Pain or Madara? well, like everything that transpires, there might be a reason..
I was thinking, maybe like when Naruto tried to learn Senjutsu, Toad Sage mode nature chakra is almost impossible to master.. and it has many dire outcomes when used/gathered by someone untrained (eg. turning them into petrified toad statues).. Maybe, just maybe Slug Sage mode has the same contraindications.. say maybe, one can't use senjutsu nature chakra for medical ninjutsu or one can use medical ninjutsu while in sage mode.. Maybe this is the reason why Tsunade doesn't use Slug Sage Mode, because she can't perform her most sacred trust.. and that is to heal her comrades in battle.. now, seeing that Sakura has mastered Byakugou, she can serve as the alliance's primary healer and Tsunade can finally got all out in battle..
if i am not mistaken, Orochimaru learned Senjutsu but his body is not suitable for it, that is why he created instead his Eight Branches Technique, him enables him to take the form of an Eight-Headed Giant Snake.. while Jiraiya learned Senjutsu, though only to an imperfect degree.. now. why can Tsunade, a scion of the Senju clan and a descendant of the Uzumkai clan can't learn senjutsu? may she learned and maybe even perfected the art.. well that makes Orochimaru (no sage mode), Jiraiya (imprefect sage mode) and Tsunade? (perfect sage mode?).. well who knows..
i will end this post with what Pain said when he fought Jiraiya..
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he said that may it be Orochimaru or Jiraiya, it seems THAT ALL THREE LEGENDARY SANNINS HAVE THEIR OWN UNIQUE ABILITIES.. i don't think Tsunade ends hers with her Byakugou.. for now, these are all speculatations.. who knows.. only time can tell..