Having had SRS can make a change in how people treat you, to varying degrees.
For most of the world, it makes no difference, since they don't know or care what you have or had between your legs. I had a couple hold-out relatives who hoped I wouldn't go through with it -- afterwards, they became resigned to reality. A few trans people might be less charitable towards you, having something they haven't been able to wrangle. A few other transitioners may finally take you seriously as your target gender; this can be a very definitional thing for a lot of people.
I think in the majority of cases, though, it absolutely makes a difference in whether you'll be accepted as female (rather than trans) -- insofar as that comes up in the milieu of a social situation. Like, taking a shower at the gym, or having sex with someone, or getting certain documents changed.