Unlikely, I think your confusing how you can set things up. You can stream the media content direct from your PC, you don't have to (unless you want to) manually copy media to the media player. Or you could download the media to a external HDD via the PC, then just plug that in to the media player and play directly from the ext HDD.
You can probably hack a realtek box and get a ftp client installed if thats what you really want but streaming from the PC would be a much easier setup.
So you want a media player with local storage which will ftp files from the internet ?
Where is the ftp server you want to access, local LAN or internet ?
NAS would work, external HDD would work, streaming would work but as OP said, he doesn't want to do those.
I'm not sure the OP understands the difference between 'streaming' and 'copying' the file. Think of it as a real time copy which you can view, bit like radio. PC is on, I can view files from the media player via a browsing menu system, I just hit play, I don't have to wait for the file to copy over then be able to play it. However as you said you don't want the PC on to watch a movie.