Database files are usually served through queries in a web form - a text field
or something similar.  As far as I'm aware, HTTrack does not create and submit
queries, so I think that this is impossible.  This software will mirror a web
site, that is, pages created in html, but not a database, which is software
accessed through a cgi script (or asp, jsp, etc.).  Good webmasters will not
allow their cgi scripts to be "readable," only executable, which means that
HTTrack will never "see" the cgi script.  It is that cgi script which will
access the database;  the database cannot be accessed through the html, which
HTTrack "sees" and copies.