Not if by "poverty" you mean relative poverty, since one of the main factors in capitalist society is inequality, and some people will always be poorer than the average. So if you define poverty in terms of average income, or the gap between the highest and lowest incomes, then it probably never will be eradicated under capitalism. But absolute poverty - defined in terms of low income, high infant mortality, short expectation of life etc - can certainly be eradicated, and possibly already has been in some developed Western countries. There is little doubt, for example, that the poorest people in Britain today would almost not be classed as living in poverty in terms of the norms of, say, 70 years ago.