I would argue that the model is useful to developing countries, even though many developing countries have so far not promoted freedom nearly as much as they have promoted economic growth. Let us look at the example of China to see a reason for this.
A key arguments in Sen's work is that freedom helps a country's economy by making people more productive. This is certainly borne out by the example of China. As China has given its people more and more freedom (the China of today is very unlike that of 1989, for example), the country's economy has boomed. However, there are still areas (such as innovation) in which China lags behind. Innovation would be stimulated by more freedom because people who are used to being free are more likely to think in the creative ways that cause innovation.
From this, we can see that Sen's model has value. It can help to account for the rise of China as well as for some of its continuing weaknesses.