Is it possible to create a new QSslSocket and for it to take ownership over the existing TCP connection, and the old QTcpSocket to be discarded, without interrupting or closing the TCP connection?

I need this to implement explicit FTPS in my FTP server, which requires that initially the connection is unencrypted, and only upon the FTP client's request (the command AUTH SSL or AUTH TLS), if it comes at all, an SSL/TLS handshake is initiated.

Yes this is possible. The simplest way to do this is to replace the QTcpSocket with a QSslSocket. The QSslSocket will behave exactly like a normal QTcpSocket (no encryption) until you call startClientEncryption. After that the QSslSocket will act like a normal QTcpSocket but all communication is encrypted in the background.

Using this I was actually able to port a 100k+ lines project to use SSL in less than one hour.

Edit

There is no (real) overhead to use QSslSocket in unencrypted mode since it will just call the corresponding QTcpSocket method. For example the read method (qsslsocket.cpp Qt 4.8.3):

if (d->mode == UnencryptedMode && !d->autoStartHandshake) {
    readBytes = d->plainSocket->read(data, maxlen);
} else {
//encryption stuff