Yes, but you will have to make sure that you state in your account deletion request that you want to immediately create a new account. The standard procedure for account deletion now is to mark the account for deletion after a 14-day "cooling off" period (during which you can change your mind), after which the account is added to a queue for deletion. The process takes a minimum of 14 days, and potentially longer. Since you aren't allowed to have more than one account at a time, having an account in "limbo" will prevent you from creating the new account. If you make your intention clear with your deletion request, staff will (usually) expedite your account's deletion.