The 100 wont make their mother not die the day earlier. So maybe not in this case. Depending on factors.

Happiness is part of the human archetype like any other emotion, and can come through all manner of stimuli, criteria. These stimuli and criteria being ever varied in humans, will make this infinitely debatable, however by the nature of us all money could/can create and be the tool of happiness. Perhaps in some of the more warped or cynical minds of men, literal money/idea of money can translate to physiological 'happiness'

So, yes it can.