Absentee ballots received by mail, except presidential ballots as provided for in Sections 23-15-731 and 23-15-733 and except as otherwise provided by Section 23-15-699, must be received by the registrar by 5:00 p.m. on the date preceding the election; any received after such time shall be handled as provided in Section 23-15-647 and shall not be counted. All ballots cast by the absent elector appearing in person in the office of the registrar shall be cast not later than 12:00 noon on the Saturday immediately preceding elections held on Tuesday, the Thursday immediately preceding elections held on Saturday, or the second day immediately preceding the date of elections held on other days. The registrar shall deposit all absentee ballots which have been timely cast in the ballot boxes upon receipt.