I recently had some bitcoins stuck in unconfirmed limbo for a while, it's taken care of, but it got me thinking... could the following happen?

1AAA is a bitcoin address. It contains 10 BTC.
I attempt to send all of it to 1BBB, but for whatever reason, this doesn't make it into the blockchain.
Presumably I'd notice that, but maybe I'm in a hurry and plan to deal with it later.
In the mean time: 1CCC sends another 1 BTC to 1AAA.
And I try to send half of that on to 1DDD.
My client believes 1AAA only contains 1 BTC so...
It would go something like txin=1AAA txout=1DDD:0.5 txout=1EEE:0.5 (the latter being my change)
But the rest of the network thinks 1AAA has 11 BTC in it so...
"Hey they didn't mention these 10 BTC, it must our fee, yay!"

Would Bitcoin-qt actually do this? If not, what steps does it take to avoid this situation?