Quite simply: No, it is not possible. A fully functioning Alfresco installation requires both the files in the content store and the data stored in the database.
With that said, you do have all of your files. The file names are lost, as is everything else about the file (permissions, creator, where in the repository they were stored), but at least you have the files. You will struggle to figure out what the files are, because they will all be named "something.bin" but if you are able to determine their file types they will be fully functional.
Sorry that you didn't have a backup of your database. That's definitely unfortunate.
