A theory floating around HN a couple days ago was that a few drinks help you focus because they are a tax on your mind. It makes your mind disregard distractions (like second thoughts etc.) because otherwise it simply couldn't function.
But I do find that being somewhat tired helps me get into a certain kind of "getting things done" zone: when the creative planning is not necessary, and mostly the grunt work of pushing things through to implementation remains.
Whenever I'm low on sleep, I'm mostly just irritable and more prone to making mistakes, although once, when particularly sleep deprived, I found myself reading the back of a shampoo bottle as if it were a cooking recipe. A couple minutes in, I realized it wasn't a recipe, thought to myself something like "Snap out of it!" Not more than five minutes later and I was reading the "recipe" again.
Anyways, personally. I'm certainly neither more productive nor more talkative when sleep deprived.