All bitaddress does is create a keypair for you, print it out and send bitcoins to the public key. When you want to redeem it import the private key to mtgox or blockchain.info or use pywallet.
The words the paper wallets use are "Load & Verify" for the (public) Bitcoin address and "Redeem" for the private key.
So yes, you simply send funds to the Bitcoin address from the paper wallet where it shows "Load & Verify".
Now, if these are gifts, what you can do is print out another copy and store it and then next year if the funds haven't been spent, you can offer to redeem (or reprint with the 2013 version, which will have something really cool I'm sure.)