I honestly don’t think it will damage leather. Too much water will leave water marks, then the bag need to be dunked to get rid of water marks. As to iron react to acid and turn leather dark, there is only trace amount of iron in city water, the little bit water leather absorbed from wet hands the amount of iron is near none.
(Also it is just my theory the dark spots appeared after dunk is because of iron in the water, it is not confirmed and may not correct, but I do suggest not to add vinegar to the dunk if any hardware is made of steel, such as the vintage
coach leather framed kisslock, otherwise during drying process , leather framed over the kisslock May turned black, depends on if the steel is rusty under the leather or not, it may still turn black even without vinegar, because the rust will have a chance to react with tannins inside leather and dye leather black, but this problem is not related to your bag)