Service to expose all encrypted messages its users sent. How protected would this data be?
To answer your primary question: Making encrypted messages accessible to everyone can be a security risk. A messaging system is typically asynchronous (meaning that you can send a message to someone that is currently offline), which makes it very difficult to provide perfect forward secrecy (great article how TextSecure solves this issue here). So an attacker with great storage capabilities (for example with a huge datacenter in Utah) could simply collect all messages that flow through your server and store them. Whenever the PGP private key of a user gets compromised, the attacker can simply go back to the recorded messages and decrypt all the messages that user received.
However, you also mention that you are assuming an adversary that can compromise the server itself. In that scenario, it doesn't matter whether or not every user can access all messages. I think it is important to first understand the goals of your messaging system as well as the different security building blocks you want to use.
Security Goals

Receiver Anonymity: By making the server a public repository for encrypted messages, you are basically creating a broadcast channel where everyone can potentially receive the message but only the intended receiver(s) can decrypt it. There exists a great body of research around receiver anonymity (e.g., this), but I am not sure whether this is actually the right approach to building your system. The problem that any kind of broadcast channel solution has is that each party has to attempt the decryption of each message, which does not scale very well (ironically, the receiver anonymity  increases with the amount of participants in the system). So regardless of whether or not the exposure of the encrypted messages to all participants poses a security risk from a cryptographic standpoint, I would not recommend this approach for a messaging system due to performance reasons.

Privacy: Using PGP will indeed provide confidentiality for your messages. However, it also requires the participants of your messaging system to have an authentic channel to retrieve each other's public keys. This cannot be the server itself, since you are assuming a potentially malicious/ compromised server setting. Threema thought of a good workaround for this problem where the server distributes the public keys but the user can verify the key's fingerprint via an out-of-band method (phone call, scanning the QR code, ...). Even if a malicious server would replace the public key of the receiver with its own, the sender could spot this by verifying the fingerprint.


Existing Building Blocks

Mixes: You can read about mix networks here. You basically achieve that a passive attacker can learn the identity of all sender and receiver but cannot link them together. This is the same level of anonymity as in your setting, as the malicious server knows who is connecting but does not learn which messages can be read by whom.

Implementation Recommendations
Have a look at XMPP/ Jabber. There exist great extensions for the protocol to offer end-to-end encryption and even OTR messaging.