She would have gone byakugou mode, and Jiraya wouldn't have to worry about her, katsuya would definitely be useful gaainst the dog summon and still provide her personal support. I'd say that two sannin being there when pein said he would have lost to jiraya if he knew his secret. It would have been gg. or at least they would have escaped with intel, both alive.
katsuya could also help her and jiraya communicate if they were not together at different points. and provide any intel tsunade may have gathered just like naruto vs pain.
Edit: I listened to his video and i see solid points. Even though i think the databooks at the time of the fight were old. maybe Tsunade would have been nearing her limit by around the time Jiraya did sage mode.
TBH though lets not forget she could have been put in a safe house or sorts (being jirayas frog) and he would go ahead with sage mode and stuff or something else. I feel like if Tsunade went with him realistically by the way kishi writes he would have somehow made jiraya sacrifice himself just as he did to save tsunade and instead of sending intel with pa it would have been with her.
Losing a hokage and jiraya would have been too much for this series. Plus Kishi has Tsunade as a blank slate at that point he could have had her whip out anything, if he had cared about shikkotsu's senjutsu he could have had her do that too but we'll never know. Shame she never got to fight pein for a bit because of editors.