Michael Clemens and David McKenzie argue so:
... common idea that skilled emigration amounts to "stealing" requires a cartoonish set of assumptions about developing countries. First, it requires us to assume that developing countries possess a finite stock of skilled workers, a stock depleted by one for every departure. In fact, people respond to the incentives created by migration: Enormous numbers of skilled workers from developing countries have been induced to acquire their skills by the opportunity of high earnings abroad. This is why the Philippines, which sends more nurses abroad than any other developing country, still has more nurses per capita at home than Britain does. Recent research has also shown that a sudden, large increase in skilled emigration from a developing country to a skill-selective destination can cause a corresponding sudden increase in skill acquisition in the source country.
Second, believing that skilled emigration amounts to theft from the poor requires us to assume that skilled workers themselves are not poor. In Zambia, a nurse has to get by on less than $1,500 per year -- measured at U.S. prices, not Zambian ones -- and a doctor must make ends meet with less than $5,500 per year, again at U.S. prices. If these were your annual wages, facing U.S. price levels, you would likely consider yourself destitute. Third, believing that a person's choice to emigrate constitutes "stealing" requires problematic assumptions about that person's rights. The United Nations Universal Declaration of Human Rights states that all people have an unqualified right to leave any country. Skilled migrants are not "owned" by their home countries, and should have the same rights to freedom of movement as professionals in rich countries.
new research reveals this to be simply unfounded. Skilled migrants also tend to earn much more than unskilled migrants, and on balance this means that a university-educated migrant from a developing country sends more money home than an otherwise identical migrant with less education. The survey of African physicians ... found that they typically send home much more money than it cost to train them, especially to the poorest countries. This means that for a typical African country as a whole, even if 100 percent of a physician's training was publicly funded, the emigration of that physician is still a net plus.