People have different experiences, I think it depends hugely on who you hang around with. If you hang around with people who have drinking problems, and want you to drink too so they don't feel self-conscious about drinking, then you may get a lot of undesired attention. Probably tends to be a bigger issue for younger folks.
For me, pretty much all my friends knew I had a drinking problem, and all were happy to see me stop, so if I ever get pressure now it's mild joking sort of pressure from folks who didn't know me back then and don't know the history. It doesn't bother me at all, but if it did I'd end contact with all of them before drinking.
Almost no one in social situations ever notices that I'm drinking soda or iced tea instead of alcohol, and if they do they don't care enough to say anything.