There's nothing that would stop you from overwriting $_FILES superglobal, but I wouldn't recommend doing it manually. And whom knows what the software is doing; GET/POST/FILES etc etc are handed to the PHP from the webserver itself, so there is no guarantee by the time it gets to where you manually insert into the $_FILES that it will go back to process.
An alternative would be to curl/socket a new request into the software, and give it the file you want to "upload". That will take it through as a $_FILES itself. That assumes the software will deal with uploads and you don't need to write anything for it.
As of PHP 5.5, the MySQL library has been officially deprecated. It is recommended to move to either MySQLi or PDO libraries for your mysql connectivity. See here for help choosing which interface you prefer: http://php.net/manual/en/mysqlinfo.api.choosing.php