How Unhealthy is it to be Sleep-Deprived

Since I already know lack of sleep is bad for your health, My main question and concern is:
Is it still as harmful if you refrain from sleep one day but the next day make up for it by sleeping extra?

Have any controlled studies been done on this?

yup

Your cortisol secretion level follows a daily night/day pattern, it pulses constantly during day and peaks throughout the night, any disturbances to normal sleeping patterns will affect this secretion pattern.

the functions of cortisol is to control your metabolic processes, cope with stress, suppressing your immune system and maintains your blood pressure

if you're always sleep deprived, you'll probably lose weight due to fat/muscle protein breakdown, suffer from depression, headaches due to high blood pressure, lightheadedness due to low blood pressure, and can easily become sick

normal sleeping patterns is also important for various other hormone secretions, also the functioning of your brain.

I'm not trolling, I'm being serious, I can't say how unhealthy except that it is very unhealthy, most of your growing is done asleep and bodily processes are done in the sleep.

Not sleeping for a long enough time can cause hallucinations.