Hi ... It's tempting but against the agmt you signed ... Not only that it's not moral or ethical ... when you bypass your current employer for a probable protective employer (in your opinion) .. that person might not have a good opinion about you ... He / She might fear taking you for breach of trust and bait n switch ...
In one of previous offices ... when an agent used the list for his benefit ... he was dismissed from the work ... the other client whom he contacted gave the info for my company ... So he has lost trust with the present too !
Hope it helps

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Best Regards