Regarding Vivenna's hair, one notes that it didn't grow or change color during the couple of weeks when she was storing her breath in the shawl, but it changed color within ten minutes of her getting it back. Vivenna thinks that that's because she was on the streets for those two weeks, and was scared the whole time...still, it's suggestive.
This doesn't really address your point, but I dislike calling breath "potential energy". The term has a specific meaning which is different from what you're using it to mean, unless you're literally suggesting that breath can be converted in a definite ratio to heat and electricity, and someone with a lot of breath should weigh more than someone with none (in accordance with relativity*).
It would make sense for drabs to live shorter lives and be sick more often than regular people, but nothing about that has been mentioned in the story (as far as I remember). It seems like if that were true, then people would be more reluctant to give up their breaths than they seem to be in the story (ie. people wouldn't encourage their kids to give their breaths to the gods if they knew that that would make the kids get sick and live shorter lives). So maybe the added lifespan/immune system boost that you get with a single breath is small enough not to be noticeable and it takes a few hundred to have any real effect.
*They wouldn't weigh much more, of course. If we assume that one breath provides enough energy for one lifeless to live for about one human lifespan (I assumed 2000 food calories per day for 80 years), and the God King absorbs 2 extra breaths per day, then he would gain about 2 kilograms every 1000 years.