It is possible but not without some special software or tools. If the drive wasn't formatted and you simply deleted a file and emptied the recycle bin you would be able to get it back with a program like Recuva unless you waited too long and it was overwritten.
Since the drive is formatted it would take some expensive software or a professional to get that file back. They use special equipment that can get data off of formatted and even physically damaged drives. The problem is that it can cost hundreds or even thousands of dollars to do so depending on the state of the drive. So to answer your question it won't be a simple procedure to get your file back.