The CHURCH, historically, did the work of caring for the poor, the displaced, the downtrodden for centuries. Prior to the establishment of “the State” the saving of Souls and the aiding of the poor, the infirm, the oppressed was the work of the Church. Courtesy of the reformation and the atheistic Enlightenment the Church was pushed out of this arena in many of the newly created countries in western Europe either by the new Protestant controlled Governments, or by the Atheists who controlled the governments like France post revolution. Catholic Hospitals, Orphanages, Monasteries and Convents continued to work where they were allowed to. Fast forward to today and the atheist secular culture has pushed the Church into the shadows in most of the developed world and these tasks have been usurped by the likes of United Way and other secular, humanist agencies with distinctly anti Christian agendas.
So no, I do not think the Church should ally or engage with these organizations. Just look at the Catholic Campaign For Human Development debacle. The Church can, and should return to these tasks under the pure teachings of Christ without compromising the Faith. To borrow a Benjamin Franklin saying, " "He that lieth down with dogs shall rise up with fleas ".
Anyone who desires can clearly see the results of the compromises of the last 55 years.