Nicholas Kristof says it does:
Smallpox was a great success but not a fluke. Among other historical foreign aid successes are immunizations, oral rehydration therapy and the green revolution.
More broadly, when we pay a few hundred dollars for fistula surgery so that a teenage girl no longer will leak urine or feces for the rest of her life, that operation may not stimulate economic growth. But no one who sees such a girl’s happiness after surgery can doubt that such aid is effective, for it truly saves a human being.
The "more broadly" here really needs to be emphasized. Economic growth is a crucial thing, especially for desperately poor countries, but it is what it is and there are other things on the table as well. To get growth, you need good policies. India, having adopted better policies, has enjoyed a good deal of economic growth over the past 10-15 in a way that no aid program could possibly deliver. On the other hand, India is still a desperately poor country and it's the kind of place where a lot of kids die of measles for lack of vaccines. Over time, if India keeps growing economically, one imagines the government will get a universal vaccination program (or something close to it) up and running, but the rich world could easily afford to step in here and help out.
The growth impact of something like that is going to get swamped by the much larger issues in play and ultimately India's success is going to be determined by Indian policymakers (and whether or not the country gets into a nuclear war with Pakistan) rather than foreign aid officials, but that doesn't mean that a well-designed program to save some lives can't, in fact, save lives.