[Apocryphon]

In my experience, being in any alternative state of mind, whether from caffeine or moderate amounts of alcohol, or even something not substance related- after working out, after a good night's sleep, after a bad night's sleep (the sweet spot is four hours), there is a sensation of productivity benefit, but I hesitate to claim there is actually productivity in every case. I think these altered states of mind help make it emotionally easier to cope with whatever the underlying cause is- possibly ADHD, possibly some variety of anxiety- and thus make it feel easier to work or engage in other difficult tasks. But cognitively? That's a whole different story.