This is a great complication to add to one's NPCs. As long as there has been stuff to mess with one's head, there have been those who imbibe in it. While a mature theme, it is essential if you want to have a 'realistic' world. Go to Comment
I view messing with time measurements a somewhat low-reward activity - you may add flavor, but you put a new layer of translation between how we are used to reckoning time, and the game world. Worse still since the game rules themselves, unless you are using a home-brew, will also use real-world time.
I see Dates as much more flexible on that front, but messing around with hours or smaller strikes me as somewhat masochistic. I'd need a really good reason for that :)