Add a file field to a block
No.

Blocks aren't entities in Drupal 7, so there's no real way to add fields to them.

If you want fields on blocks, then take a look at the awesome Bean module.


  Beans were driven by the API first. This means that you can create
  block types (bean types) all in a plugin class turning off the UI. The
  entire configuration in code. No worry about feature reverts.