The answer depends on the way you do it. If you use public-key cryptography
]) (such as RSA) and do it right, nobody can read the message after is read and discarded by a client; being administrator or not is irrelevant here.
If you use any single-key system and send a system over internet… how can it be secure?
A communication is totally secure it a receiving party generates both keys and sends an encrypting key as public. Both server or other client part get only the public key and can encrypt a message, but it can only be decrypted by the party who generated the key, as a private key should not be sent anywhere. In other words, the party which uses a key to encrypt message cannot decrypt its own message — this is the whole idea of the security based on a public key.
So, how to archive unencrypted messages for later search, etc.? It won't be a problem if you have only two parties, without a server (or if a server just transmit encrypted messages transparently). The parties exchange two pairs of keys (four altogether). Each sending party archives the message before sending (as it will never get a key to decrypt its own message; it can only decrypt the counterpart's message), and each receiving party decrypts and archive decrypted message after it decrypts it. Everything is symmetric. This way, each party can archive all messages passed on one-to-one conversation and cannot read any messages from other parties; moreover, nobody in the middle who could spy on messages could not decrypt any of them. Even the server.
Here is why we can trust such servers! Imagine that the server's behavior is totally hidden, but the client software is Open Source (this is the only way when you can use 3rd-party service and trust it no matter what it does). Analyzing this source code, one can make sure that only public keys and encrypted messages are sent. From this fact, you can be sure that your messages are not decrypted in the middle. Of course you can trust your companion on the other end, as this party could disclose your public key to someone who could impersonate your counter-part; but this is a different problem — you could solve it using digital signature
of the data, which is the opposite to encryption, please see http://en.wikipedia.org/wiki/Digital_signature