Yes, if he has the chaincode.
1x Root Private Key
1x Root Public Key
1x Chaincode
A watching-only Armory wallet is just
1x Root Public Key
1x Chaincode
So basically watching-only wallets don't have any private key data at all, and the chain code is just a constant that is carried through all the calculations. With the priv key + chaincode, you can compute all private keys. With public key + chain, you can compute all public keys that match the private keys produced on the full/offline wallet.
The chaincode and public key are not security-sensitive. Someone getting them is a breach of privacy, not security. All internet security is based on the fact that the public key is widely distributed (i.e. "public") and that the scheme maintains full security as long as no one else has the private key.
But I don't spend much time worrying about this. We do not support or claim to support any use cases where private keys are intentionally revealed. And if your wallet is unintentionally compromised, they will all be revealed anyway.