I think it might, not right now but maybe one day when it is fully accepted worldwide and we don't have to pay huge fees to banks and other financial institutions to keep/transfer our money from one place to the another.
Not saying it will magically solve world poverty but some people when they pay less for maintaining their funds, they might spend a little more on charities.
Poverty is an over grown global problem, there are a lot of factors that contributes to poverty, like, corruption, war, illiteracy and the unbalance distribution of wealth. Do you think bitcoin can overcome all of these contributory factors? Poverty is like an illness that cannot be treated overnight. It needs a lot of major reconstruction on the economy and market system. Maybe bitcoin can be considered as one of the solution, But it will take a lot more to solve World poverty.