Apparently, if you accidentally cut yourself with a knife while drunk (not an unlikely event) and you roll well on the d6, the knife bounces off of your skin. Just more evidence that hit points are covering too much territory (physical, psychological, and metagame).
The only way to cut yourself with a knife is pure DM fiat. If the DM fiats something that doesn't make sense, that's his own fault.
But it would be trivial to explain as "your own poor grip on the knife means it doesn't actually do anything".
I'm not a fan. You might not feel the pain, but the damage is still there. And what about HP as tuning a fatal blow into a near-miss. I don't think that gets easier when you're drunk.
As the rules clearly state, HP do not only represent physical damage (and minor physical damage does not necessarily imply reduced HP).
Also, it is very well known that being drunk quite literally turns fatal injuries (in car accidents) into non-fatal injuries. I don't see why that couldn't apply to combat injuries as well.