I think most cops know the difference between intoxicated and not.
where I would be more concerned is if you get into a jam and have to use your gun in self defense, and the guy you shot or his estate sues you claiming wrongful death/civil liability and then they can find witnesses placing you drinking alcohol within the same hour as the incident, that may be a legitimate concern....
I don't take my gun when I go to bars, Washington law says I can't carry in a bar and I don't even bother leaving it in the car, i just leave it at home.
if it's a diner or restaurant like Godfather's Pizza that sells beer on tap I have a soda or a water instead if I'm carrying. I don't need there to be any question that I was sober or not if I get in an incident. see what will happen is you'll get into a trouble, pull the gun, the cops will say "ok you look justified" and they recommend not to prosecute, prosecutor declares justified. well then the guy you defended yourself against will get a lawyer who will find people who say "he was drinking the night he pulled a gun on that guy" and this will come weeks later and there's no way to prove if you were intoxicated or not, so the civil jury will see guy, possibly drunk, armed with gun.
not saying it's likely, but it's something I worry about enough to avoid the alcohol scene altogether while armed. that's just my personal opinion though.