If anything, over the last several years, what I've found is that stress is far more likely to hurt relationships than intoxication. After a frustrating day, I'm way more likely to be clipped, snippy, abrupt, or unhelpful. That's the stuff that clients and customers remember.
I drink pretty regularly and can't think of a single time that intoxication has harmed a business relationship (indeed, I routinely take clients out for beers, like most other businesspeople do --- if alcohol and "loss of inhibition" was such a force for chaos, one assumes this would be less of a time-honored tradition).
On the other hand, I can think of many times where stress has damaged relationships, sometimes permanently.
I picked 2-3 drinks out of a hat. I know the guy who wrote this post drank 4 glasses of gin before getting on a plane (I'd throw up if I did that; alcohol and air travel don't mix with me), but 2-3 seems like a pretty reasonable casual evening of answering emails.