The way you are dressed definitely influences gate agents when it comes time to "bump" people into business class when coach is overbooked. A very good friend of mine who worked for AA told me that the nicer your attire, the better your chances are of being offered an upgrade.
This tip paid off for me on a full flight from LGW to DFW. My friend had told me that coach was almost always overbooked on this flight and that if I was interested in an upgrade that I should wear a sport coat, tie and decent looking shoes and identify myself to the gate agent as being interested in an upgrade to business class if coach was overbooked.
Sure enough, I was one of eight coach pax offered a seat in business class that day. Every one that was offered this upgrade was dressed in what was considered to be business or business casual attire.
On the other hand, I was bumped up to first class on an Eastern Airlines flight back when I was a poor but honest, jeans and sneakers wearing college student, just because I was willing to cooperate. Our 722 had been held for about 20 minutes past scheduled departure for a dozen or so connecting pax. When they finally boarded, the FA's discovered that 3 of the connecting pax had been issued the same seat assignments as pax who had already boarded. There wasn't a seat left in coach and two guys were making a stink because they were supposed to sit together. Everyone else was ready to go and things were really starting to get ugly when I told the FA who was trying to settle things that I would gladly move my seat if it would help. She smiled and thanked me, asked me to get my carry on and then proceeded to usher me up to first class where I was treated like royalty. I was seated next to a high powered business type who gave me the once over and then went back to his Wall Street Journal. The guy never said a word to me during the entire flight. I wasn't smelly or obnoxious, but I think he resented the fact that I was obviously sitting somewhere he didn't think I belonged.