When I was young the only ill effect I noticed after not sleeping for a whole night was ordinary but more intense tiredness towards the end of that following day. The morning didn't feel any different from normal, which surprised me.
These days it's rather worse. If I'm underslept I have some nausea from the moment I get out of bed, I feel as if I've consumed some kind of poison, and my brain function is impaired to a degree. It's harder for me to concentrate. I start to get mild double-vision. Not surprisingly, my mood usually takes a turn for the worse.
I can't sleep unless I'm lying flat, nor can I sleep at an airport, so when I travel between London and Memphis (which I've done 7 times there and back, on my own, since 2013) I'm awake for at least 35 hours, but surprisingly I've always mastered the adventure in spite of all the curveballs it throws at me which require a lot of good focus, rapid decision-making and social skill. How? They say a little bit of stress helps people to function. I wouldn't call the stress I go through little, but with a lifetime's experience in managing stress I can cope with quite a bit of it, and I think the adrenaline (or whatever it is) helps me to keep me alert for solving the problems and possibly acts as an analgesic. Of course I know that however badly things go wrong I'm not likely to die through incompetence. The task is so important and demanding that it distracts me from all the crappy sensations I'd experience from being underslept if I were just slobbing about at home. It's amazing what people can do in an emergency.
It's no use as a general intervention for the ill effects of being underslept of course, and I wouldn't recommend anybody jumping into the deep end of life as a remedy (I suspect it might occasionally work but it sounds rather dangerous). But if an underslept person who can't simply sleep it off can find something reasonably safe and fascinating to do, the resulting hyperfocus might distract some people from those symptoms, to a degree at least, if the symptoms aren't too intense to allow that to happen.