Hm - just depends on HOW (I could think of very clever logics here, despite I'm not Satoshi) it's done - and I guess price reaction will be short termed and could also be part of the logic to e.g. REMOVE some volatility...
the magnitude of the effect on price would depend on the amount spread which you have in mind. but how many poor are we talking about or how much bitcoin per person?
the only possible way that can be good and effective in my opinion is donation to a "charitable organization". i have seen a couple of them in DogeCoin community but never seen any in btc.
I'm just trying to really think decentral - so an 'organization' is only good, if it's on the very low level, say a leader of a very small group / village in e.g. Bangladesh or so - because that 'small' guy feels really responsible for his few poor people next door and no overhead costs are spent at all.