Wearing them in the mission makes the mission easier, as you can get to Anthony Corrado's room without getting a wanted level, and if you move fast enough, you can get out of the room and to the lobby before getting a wanted level. Not taking them will make the mission harder, as you will get a wanted level before you get to Anthony. Getting the Scrubs after the cops have seen you once is useless, as they will recognize you and give you an immediate wanted level. After the mission, the scrubs serve no purpose.