Yes, absolutely yes. Poverty to me is the state of the mind. Poverty is not impose on any individual but accepted by an individual by desire.
Equal right was given to all at birth but environmental factors will alway play a vital role at every point of growth in the life of every individual. Being poor does not mean not having much money because money is not happines but not finding happines is poverty.
Hence everybody can be rich if and only we realize that lack of money is not poverty but lack of happiness is poverty.
Where are environmental factors and population in your classification of poverty as emotional abbreviation? Happiness and sadness don't represent wealth and poverty but it is inherent emotional tendencies posed on the ability to feel satisfied. Even a poor person could be happy having just a meal per day and his rich counterpart could be sad having triple square meal a day.
To the OP, it is not totally possible to eliminate poverty even in countries where their economies are very viable, there are homeless people, people still starving due to one environmental factor or the other. So, I can't say poverty can be totally eliminated.