I never drank on the job while at work, though there were times I drank while working from home just to keep things "even." And certainly plenty of times my last drink was at 5am, so there were definitely times I must have had a certain scent about me.
I'm convinced that people noticed but 99.9% of them were too afraid to say anything. Not in an afraid of me sort of way, but in an afraid of a really uncomfortable situation sort of way. Easier to ignore it than to confront it. Also (I know this sounds egotistical), I'm a stellar employee. It's kind of like the downside was worth the upside - to them.. I sort of retrospectively wish it wasn't that way. I mean, it would have been mortifying for someone to call me out, but my work is So Very Important to me that I think I would have come to my senses much sooner than I did.
p.s. I'll bet that client had no clue why your hands were shaking. Most people seem to be oblivious to the tell-tale signs we all know well.
O