The passphrase is stored as part of the wallet.dat file, so yes, that should work, as long as you haven't received any payments to addresses with private keys that don't exist in the old wallet.

Note that these received payments can actually occur when you send a payment, as a hidden "change" amount is sent to an unused hidden private key which is stored in your wallet file. Your old wallet file should have had stored 100 of these generated in advance though, which means you're probably ok as long as you haven't used more than 100 private keys since your backup.

Most payments you make will use one of the pre-generated private keys, as will each receiving addresses you create.