That's not what I meant.
If I understand correctly, right now, when a client of the cluster computes a block, that block is sent to more clients by the server as a proof of work (that is, to see that they actually compute). If the block is first broadcast into the Bitcoin network (not the cluster clients), a malicious cluster client could recognize the proofs of work. But on the other side, if it's first proof-of-work'd by the clients, then the server could spend seconds, even minutes before all the (connected) clients answer the check. If in that time a block is generated and broadcast in Bitcoin, ours would probably be invalidated (that's what I meant by "steal").
No, this is not possible. Every worker gets unique sources for hashing, so when he found nonce which makes correct proof of work, it is definitely not valid for other jobs.
EDIT: Oh, I still don't understand your question. My answer was about broadcasting single PoW on low target between clients before submitting to cluster.