You wouldn't be able to double spend. If it were that easy people would be backing up and restoring their wallets sans crash and double-spending like crazy. Your wallet.dat holds the keys you are allowed to sign with, which are essentially account numbers. The transactions themselves are stored in the block chain, which is updated upon restart of the client. If you attempt to send bitcoins that you no longer have it will fail because every client in the distributed network will have a copy of the blockchain in which you've already spent that money.
You are correct that network will not allow me to proccess the transaction, however using the old wallet file i am being seen as an attempting double spender, even though unsuccessfull. There is no reason for this. I should be able to update my wallet file to be in sync with the network.