If a transaction simply contains a list of inputs and outputs and are not tied to tied to specific blocks.. it seems to me that Bitcoin-QT should be able to sign a transaction (and subsequent transactions) without having the updated blockchain. Or, will Bitcoin-QT not spend unconfirmed outputs?

If it could spend unconfirmed outputs, then you should be able to perform a transaction and dump the raw transaction output... burn it to CD and copy the transaction to an on-line Bitcoin-QT installation and re-broadcast it. Could this work?