Not really. I know it's not your question, but if you want to kill them, a bucket of water will do. They won't be able to climb up the edges and will eventually drown. Many mousetraps use food dangling over a bucket of water to kill mice.
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yes they do. It is instinctive. If you put one in water it will swim but if it can't get out of the water it will eventually tire and drown.