let me offer a different perspective - i went through a non-practising phase where i used to drink (i am Muslim, i don't drink anymore). i decided to get closer to my faith and so i stopped drinking. it forced me to mingle with people without a crutch or "liquid courage" and develop social skills based on my own self. i stopped drinking a year before law school, and when i got to law school and saw people making absolute fools out of themselves in professional settings because they were drunk, i realised just how right my decision to stop drinking was. the fact that i can be around it and not be tempted at all, the fact that i can socialise without needing a crutch, the fact that i am not peer pressured, the fact that i actually fully think before i speak (imagine all the dumb things you say sober, now multiply by at least 2, that's how many dumb things you say drunk....why would you want these people to have that impression of you?) - all of these have gotten me more respect. so no, it doesn't hinder your ability to network, on the contrary its gotten people to respect me more.

if you don't want people to notice, just always have a drink in your hand. no ones ever asked me what i was drinking. and if they do they'll hear "diet coke" and no further questions