It does, because there's just something about a female chest that can't ever be properly hidden no matter what you try. Even the smallest ones are "noticeable" compared to a male chest. I've always felt that there must be an evolutionary reason for female humans to have a permanently enlarged set, compared to most other female mammals who don't. They are very "in your face" socially, so to speak, and unmistakable. There's plenty of theories about why, but either way, it's very hard to be considered male whilst having a prominent pair.
The main thing I noticed after surgery is that I don't think about them, or that they are gone. They are absent from my mind, which I think means that I'm back to the default state my mind always believed they should be in. I assume it feels just as 'default' for most MTF to have them than not.
Running and most activities are a great deal easier. I am definitely more hydrodynamic, now.
As for being one of the guys... the chest is a very important part of feeling right here. Just the fact of having boobs makes a big difference in how people can act, dress, look at you, and how easy it is to do things. It does feel much freer to have my chest back. I haven't thrown my shirt off in public at this point as I'm not a sun lover and not much of a lover of crowds of tourists either, but I may well when the summer comes in take a walk in the evening on the cliffs without it. That'll be a first in... well, for ever.