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").