FTP works mostly the same as any other TCP/IP-based service. Even if you're only uploading files, the communication is still bidirectional, both at TCP level (packet acknowledgements) and at FTP level (responses to various commands that have to be issued before the upload can start). For this to work, the server must know the client's IP address, otherwise it couldn't establish even the basic TCP connection.
So that means you cannot make the file appear out of nowhere; the only thing you can do is borrow someone else's IP address – e.g. by using a VPN service, or Tor, or a SOCKS proxy, or a web-FTP gateway. If you trust that your selected proxy or VPN doesn't keep connection logs (to correlate the packets from both sides), that would give you some relative anonymity.
Meanwhile, there is no specific "computer hardware ID" used in any of those protocols, with the one exception of IPv6 addresses frequently having a MAC-based suffix (depending on OS settings). This usually won't be a problem if you're proxying the connection through someone else's address anyway.