Yes. Welfare programs are full of government employees who administer the fiendishly complicated rules about how much people get and why. The EITC relies on the poor people to figure out that they're eligible and do the math themselves. It certainly costs the government less, but by transferring a lot of the work to people who may not be as well-equipped to do that work. A government bureaucracy can be incredibly wasteful, but at least its employees probably have high-school educations, aren't working other jobs, and can specialize in learning all the silly rules -- they only have to learn the rules once, and can apply their knowledge to thousands of cases. Low-wage people may be badly educated, are definitely already doing other jobs, and have to each separately learn how the whole thing works.

All that said, though, the EITC is so much simpler than almost any other anti-poverty program that it's still likely one of the most efficient around.