I don't know whether it would show up or not, but regardless, the marriage license application is a sworn document, and you have to certify under oath to the clerk that you are not currently married to another person and have not been divorced from another person within the last 30 days. If you lie on it, you're committing perjury, and also the validity of your new marriage may later be called into question. You're free to remarry on the 31st day after your divorce was granted.
