Yes, it can happen-though it'll show 0, it's lower. I've even had it to a point where a Stone of Happiness got a 'zeroed' girl to 9. Think about that, please...
It's obnoxious to have to pull them out from there. Even the most attentive can miss things, and it ends up in a spiral of sorts, as being a Drug Addict stops happiness gains till it's cured and lowers happiness in itself every day they're without a fix, and is CAUSED by low happiness, which means it'll come back again.