It is not simply "signing", it is spending valid payments you have previously received.
To clarify - I would only be redeeming outputs that were previously generated on this off-line Bitcoin-QT instance. I would not be redeeming outputs that other third-parties may have sent me, but rather outputs that I have only signed myself. I gain no further information by downloading the blockchain, other then seeing which block my transactions were accepted in.
I suspect Bitcoin-QT won't let me spend unconfirmed outputs though? I know of at least one web-wallet that allows this. I would simply like to use the core-dev client instead, off-line.
You can create and sign transactions offline. You will need the txids and vouts of the inputs, the script pub keys and the private keys of the input addresses. IF you have all of this you can craft a raw transaction manually. But you can't do it with the GUI.