My answer is essentially "no", with a few small qualifications. Posner gives the main arguments against aid, so I will not go over them.
William Easterly among others has written several articles that examine the empirical evidence on the relation between foreign aid and economic growth-see for example, chapter 2 of his book The Elusive Quest for Economic Growth. He and others have discussed foreign government aid to countries in Africa, Pakistan and other Asian countries, and typically have not been able to find any noticeable positive effects of aid on a country's economic growth
In this book Easterly discusses in detail aid to Ghana in the early 1960's that helped it build a huge dam and the largest man made lake in the world. This project was at the time supported by some economists with extravagant claims about what it would accomplish: create a new fishing industry, generate electricity, encourage a new aluminum smelting plant, and other benefits. At a huge cost, it accomplished few of these goals-there is a smelting plant run by a private multinational that has had slow growth in its output- but little else that is positive. Indeed, the lake had some serious negative consequences, such as destruction of considerable agricultural land because of the wide area flooded, and the importing to those living near the lake of water-borne diseases, such as malaria, river blindness, and hookworm.
India is my favorite example to illustrate the failure of government foreign aid. From the fifties until the end of the 1980's more private and government aid went to India than to any other country. Yet during that same time period, India had a very modest growth in per capita income of about 1 percent per year-sometimes resignedly called in those days the "Hindu rate of growth". I am not claiming that foreign aid was the main source of India's mediocre performance, but it clearly did not overcome the bad economic policies of its government. In fact, aid may well have encouraged these policies as the India government could always count on foreign aid to help it out of the worst aspects of any mess caused by its restrictions on foreign trade, severe controls over private investment even by Indian companies, and neglect of basic education, roads, and agriculture.
Fortunately, in the early 1990's, the Indian government recognized that the real cause of its economic problems was not insufficient aid, but its own policies. Reforms at that time include opening up more investments to the private sector, greatly lowering tariffs, quotas, and other barriers to foreign trade, and changes in its thinking about relying on rich countries to help its development. Indeed, India can legitimately claim that now one important obstacle to its growth comes from the very same rich countries which had been important donors because of their import restrictions that hinder the access of Indian farmers and manufacturers to their markets.
Foreign aid programs other than of a humanitarian nature are destined to fail because they involve transfers of resources from one government to another. No economist who has closely examined the evidence concludes that the reason why some poor countries fail to have significant economic growth is because their governments have insufficient resources. The complaint is typically that governments do the wrong things with the resources they have, including their regulatory powers. They discourage entrepreneurship, give cronies special advantages in investments or in rights to import and export, over-regulate labor markets, spend too much on public prestige projects, such as domestic airlines and large dams that of little use and yet drain valuable resources, neglect basic education in order to create expensive universities, and so on. Foreign aid only makes it easier to continue to promote projects and policies that are not merely neutral with respect to growth, but hinder any take off into rapid growth.
Donor nations are also subject to political pressures that influence the form their aid takes. They attach various strings to the aid that help powerful interest groups in their own countries at the expense sometimes of the aid having any chance of helping recipient countries grow faster. Given the distortions away from effectiveness on both sides of the donor-recipient equation, it is no surprise then most foreign aid has been at best ineffective, and at worst negatively affects the growth prospects of recipients.
Does my discussion mean that I oppose all foreign aid except sometimes for military assistance, and for humanitarian purposes? My answer, to repeat, is yes. However, I include in humanitarian assistance aid to combat some of the major diseases in poor countries, although I prefer such aid to be from private foundations and other groups since they tend to be more effective than governments -see my January 1 post on private charities. However, if governments of rich countries do give resources to help fight diseases in poor countries, they should give to private groups in these countries. If they have to give to government agencies, they should stipulate in the grants that recipient governments have to match their own tax revenues in specified proportions to the amounts received in aid.