Best we can tell from the developer documentation, currently the Tableau Data Extract API (http://onlinehelp.tableausoftware.com/current/pro/online/en-us/extracting_TDE_API.html) allows you to create new TDEs, but has no method for appending to them.  The lack of a way to append via the API makes its usefulness limited for cases where the TDE is large and needs to be incrementally updated frequently.