I have a couple of psychedelic experiences that were undertaken with a sleep deprived brain. These were all unintentional; I don't see any possible benefits of being sleep deprived while tripping. In fact, one of these experiences was EXTREMELY UNPLEASANT. And that is an understatement. You know that feeling just being behind on sleep where it feels like your brain is tired? Well it was like that times 10. I smoked some cannabis at some point in this EXTREMELY UNPLEASANT experience and basically went psychotic for the last bit of my trip. I could "physically" feel my brain frying like if you had dumped coffee on a circuit board. Every thought sent this fiery very real sensation all over my brain. And this lasted for hours. I was utterly convinced that my brain was going to short circuit and I would die. NOT fun.
With that being said, I am very sensitive to my sleep schedule and need more sleep to function than others, so others may or may not have better luck with this.
Once in a while, you get shown the light in the strangest of places if you look at it right.