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.
header('HTTP/1.1 420 Enhance Your Calm');