Yes, you can recover a file that you deleted a month ago. However, the chances of the recovery being successful are very shallow. That is when you delete a file on a hard drive. It is not deleted from it unless you write new data in place. For a drive you've been using for a month, you've probably written some good amount of data already, which will hamper the chances of file recovery. The best situation will be when you haven't used the drive after deleting the file.