NO IT DOESN'T. I'd assume some does due to the dying organisms in it, lol. Borax is anti-fungal and anti-pest agent, used widely in agriculture in some countries :)
I use my Distilled water, and with 1/8 of tsp of Borax it came exatly to pH 7. Tastes quite good actually. Doesn't smell much, except very faintly when I drink it = it resembles slighly to bicarbonate. But more pleasant.