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).
No. PoW is checked directly on server. No job resending.
If the block is first broadcast into the Bitcoin network (not the cluster clients), a malicious cluster client could recognize the proofs of work.
Why should cluster client go directly to bitcoin network? If proof of work is valid, it's 50BTCwill be received by server, not client.
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").
It is already possible that some miner find valid block and until he submit it to bitcoin network, somebody will be before them. Yes, in this case block will be invalid. But there is almost no latency between sending PoW from client to bitcoin network, if block is found.