No.  The IRS' schema only allowed that with e-filing.

Your client may, however, use the links on this IRS webpage (https://www.irs.gov/payments) to make electronic payments.

If your client would like to schedule ES-tax payments more than 30 days in advance, he/she would have to enroll in EFTPS (https://www.irs.gov/payments/eftps-the-electronic-federal-tax-payment-system).