No. The blockchain is the transaction log.
A way to think of it is you don't have any coins
. The coins are in the blockchain. Every single coin ever mined and every coin that will be mined is in the blockchain. The block chain is a consensus on where the coins are currently located.
It is like a digital version of the giant rai stones.
The stones were used for currency but they were never moved. The consensus of villagers determined who owned it. When one entered a transaction involving the stone everyone was notified and the consensus was updated. Bitcoin works the same way.
You use private keys to move coins.
Private key = proof of ownership
Private key = ability to sign a tx and move a coin to a new address (spending coins is just moving coins from buyer to seller)
No private key = no move, coins lost "forever".
There are methods of regenerating private keys. The term is a "deterministic wallet". With the secret seed you can recreate the entire wallet because the keys and their sequence is always the same from the same "seed". No need to backup anything but the secret and backup could mean recording it offline like on a sheet of paper. The default client (also called the satoshi client) is not determistic. You will need to routinely backup your wallet as it contains your private keys. The wallet.dat contains other "stuff" which improves efficiency of the client but the private keys are what is important. Everything else can be regenerated if you have the private keys and access to the blockchain.