There is no builtin mechanism to do that, but is it easily possible to hook yourself to the navigation url pattern and perform additional work when downloading the file, like storing logs via the audit service.
Note that files can also be served by a servlet (that handles big files more efficiently), and that there is a number of additional ways that you can retrieve the actual document (export via clipboard for instance).
Note also that some non-binary content can be served as downloadable files sometimes, so depending on what features/screens you're offering to the user (and the kind of "audit" or "control" that you'd like to perform), options can be different.
