Is it possible to write a servlet that acts as a FTP server?

Yes. It would spawn a thread that opens a ServerSocket, then listens for incoming connections and speaks the FTP protocol.

Unfortunately I don't know of any source for FTP Server code. You may want to look at http://www.jguru.com/jguru/faq/view.jsp?EID=107270 for more information.

Generally, extending servlets to protocols other than HTTP is a quixotic enterprise. Just install a standalone FTP server and you'll be much happier.