How do the Federalists relinquish power in 1800 if the country is not "democratic" by then?
The Federalists lose because South+Middle outweighs North. I don't see what that has to do with whether the government is popularly elected or not.
Even if you argue that the South and New England were undemocratic (going along with the interests of the planter and merchant class, respectively), which is of course ridiculous, clearly the Middle voted Republican only because it was democratic. New York was Republican precisely because Burr built a democratic coalition there.