no, it will not remove the poison within her, but the power of her jutsu would neutralize the effects of the poison as long as the jutsu is active.. constant damage is negated by rapid healing.. an also, poisons like any other drug is synthesized by the liver in the long run (granted that the individual survives the ordeal)..
Then you are claiming that the Salamander is slow in taking effect. Read the edo version of Hanzo's flashback. It rapidly paralyzes the opponent. It's now a battle between rapid poison effect vs rapid healing. Is it contently battling each other.
also, i think you are taking think conclusively.. you are thinking of a scenario where Tsunade has already been poisoned.. granted her expertise in the medical field, it is safe to say that she knows how to deal with poison masters.. also, being a medic, i'm sure Tsunade has already prepared antidotes for a wide array of poisons.. poisons can be neutralized by different antidotes which affects the same area which the poison destroys..
Hanzo flooded the field with poison gas during the war arc so yes she will eventually get poison. So therefore I am right about the preparation, she needs preparations to win this battle. I already concluded that if prep antidote is in this battle she win this fight. But if someone were to make a vs thread for this battle and restricts knowledge how is gonna know what to prepare with no knowledge on who she is fighting
saying so, even if where to be poisoned, she would still have enough still to deal with Hanzo before creating an antidote (she doesn't have one already).. besides, basic effects of poisons affect normal organic functions such as destroying cardiac cells, affecting intercostal muscles thus preventing breathing, destroys antigens in the blood causing internal hemorage, etc.. Tsunade's vitality alone has shown to withstand those effects with using her jutsu.. i think i wouldn't be a problem once she activates byakugou..