No. However there are a number of services that analyze Appstore data and attempt to guess the number of downloads for specific apps and categories. Most of the detailed information is pay-only, keep in mind for iOS apps, this is all based on guesswork since Apple does not release detailed data for the entire store.

http://appannie.com
http://www.statista.com
https://prioridata.com

For the education (free) category, an app that I worked on reached the top 25 with ~1,000 downloads a day. The bar is higher now across the board.