I've heard of a few death row inmates who stayed up the entire night before the execution while most others I guess would sleep at least some before the execution date.
I would never do anything to get myself on death row or in prison for that matter but if I were gonna be executed then yes I would stay awake the entire night because it's not gonna harm your health and you won't be awake that much the next day when they execute you.
So you might as well be awake and alive and doing something in your death row prison cell before you go to sleep permanently upon execution.
It can be hard to stay awake if you're really tired but I've seen a few death row inmate pictures before there execution and they were really groggy the next day when execution became and I'm sure the death row inmate has trouble sleeping when it gets really close to the day that they are gonna be executed.
I know I couldn't sleep at all knowing that my death is getting near as I'd want to be awake as much as possible before my heart stops beating for good and before my eyes close for good as well.