i don't see how drinking would lower the success rate of hanging or jumping since all you have to do is drop down.
It lowers the success rate of falling for sure, not sure about hanging. Impact is spread easier through a relaxed body. When you panic and tighten up your body bears more of an impact in the area of impact rather than the entirety of the body, it's why you can more easily break your leg when landing on them from a jump without bending your knees.
High enough heights it won't matter, but most of us would have to make do with what we have. The reality is tgat we are unlikely to land on our heads as we'd likely plan as we begin to panic, so how the impact spreads is important.
While one might think spreading it throughout the body would be better, it's diminished throughout the body rather than concentrated. Better to break the impact forcefully and continue to have it damage the rest of your body that would no doubt follow afterwards rather than spread as quickly to the rest of your body.
This is also why drunk drivers tend to have a higher survival rate in accidents than their non drunk counterparts.
When tense your body fights the impact (causing more resistance which in impacts greater than it can take is good for the suicidal). When loose it goes with it.
As for hanging, I have no clue, but it might make your neck muscles less likely to tighten which may or may not change the time needed to properly die.