Mhm, good question.
For your first question, I think they might, not because they lactate, but you don't want it dripping wherever you go.
I think that breasts would still be "indecent", as men find them attractive, and since they are too, sadly, linked to sex, would not be changed much.
Western culture is very uptight and reserved about the human body, and the certain areas won't probably change.
So pretty much, they would, but maybe not for the purpose you are thinking of.