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Yes, you can deposit them directly into your account. Keep in mind that the checks likely come with a 3% or 5% fee, so for instance if you deposit a $5000 check, you would owe $5150 or $5250 with a 0% offer.
Edit: It counts as a promotional balance transfer, not a cash advance. With the fees, if you paid it off in 2 months that's the same as getting a cash advance with a 18% or 30% APR depending on the fee.