Was the Louisiana Purchase an example of Jeffersonian democracy?

Yes, the Louisiana Purchase was an example of something
that was done to further Jeffersonian democracy.  The reason for this has to do with
Jefferson's vision of what America should be.

Jefferson
believed that America should be made up of small farmers.  Such people would be
self-sufficient, making all that they needed (or almost all).  Jefferson thought that
only self-sufficient people could be good citizens of a democracy because no one could
ever tell them what to do.  (If you can get your hands on Farmer
Boy, by Laura Ingalls Wilder, you should look towards the end of the book
where Almanzo is offered an aprenticeship with a prosperous carriage maker.  His mother
flips out because she wants him to be a small farmer so he will never have to rely on
anyone else.  It's my favorite statement of Jefferson's
ideas...)

Anyway, back to the Louisiana Purchase... 
Jefferson thought that all that land would allow many more Americans to become small
farmers.  That would prevent the US from becoming some big industrial nation with lots
of people working for other people (and depending on
them).

So, the Louisiana Purchase was an example of
Jeffersonian democracy because it was supposed to allow Americans to be self-sufficient
small farmers rather than dependent wage laborers.  This was Jefferson's
hope.