Some people probably deal with the deficits better than others, but all of the "positive" results from something that extreme I've heard of are subjective and self-reported, so not worth much as evidence. There is, however, lots of empirical data about loss of cognitive function due to sleep deprivation; to be fair I don't think any of the studies I've seen targeted precisely that (self imposed, cyclic) sort of pattern. On the other hand, none of that research suggests a good outcome would be expected. I'm not referring to all sleep patterns here, just those that rely on very short cycles, e.g. 20 min.
Last time I asked this was: https://news.ycombinator.com/item?id=6258098 (thanks https://hn.algolia.com ) and, well, the score I have for this remains at "zero accounts I trust", even from this relatively interested forum.
(Caveats: I recognize there is significant sleep variation in humans. Science has confirmed this, even if it doesn't know why. I also believe in "bi-phasic" sleep of shorter nights and significant naps, again, this has been established reasonably well. This isn't generalized skepticism, it's specifically the Uber & other variants that I've never heard even solid anecdotal evidence for.)
I tried a 28 hour day cycle (awake for 20 hours, asleep for 8; 6 day week) for a few weeks when I was in uni (as Mondays through Thursdays had me awake at relatively normal times and this suited my lecture schedule at the time) but then other obligations knocked me off schedule for a few days and I reverted back to normal. I feel like it could have been successful longer term, but I didn't do it long enough to know for sure. I guess the hardest part is making sure other things don't interfere.
It's just that there does not seem to be any hope of doing it indefinitely. Sad. My personal biases and desires, like many here, lead me towards really wishing it could be, but I just don't see the evidence.