Can object history tables be exported via MassEffect?
Yes. There is an operation available called "Export" which will show ALL tables in Salesforce including those that are not directly modifiable. Once Export is selected the History tables will be shown and can be exported like any other table (right-click to bring up the export window).
Note on Date Fields:
To export changes from a particular date, use the CreatedDate field. For a specific day, 2 conditions will be needed since this is a Date/Time field, e.g., CreatedDate >= January 1 2014 12:00 AM and CreatedDate <= January 1 2014 11:59 PM
More information on creating conditions can be found here.