I cannot think of any advantage to "wiring" the funds versus sending a payment through your bank's online billpay service. I think your real question is whether Chase will temporarily increase your credit limit by the amount of any overpayment.

Bear in mind that if your card is a VISA Signature or MasterCard World it has a "no preset limit" feature, and the stated limit pertains only to the revolving line. You can exceed that line without any adverse consequences, but what you cannot easily know is the precise amount the issuer will allow you to spend.