What do you mean by "is it OK?"
CAN it be done? Sure. Is it legal? Yes.
Will CC#1 decide to close your account for playing games with them? They might. Credit card companies are running scared right now, and anything that looks like the customer is having money trouble makes them nervous. Some of them are closing account or reducing credit lines on customers who never were late, never missed a payment.
If you do get a BT offer and use it, even if they close your account you can still pay off the balance in accordance with the BT terms.