Is Tyrion’s contempt for democracy historically accurate?

Yes. Hell, the word “democracy” was pretty much a pejorative until well into the 19th century – per

Thucydides and other classical political theorists (thinking primarilyabout the concept of kyklos here), democracies could only function in small, homogenous city-states and were prone to collapse. 

There was the revival of Renaissance Republicanism, although these republics were quite oligarchical and wouldn’t probably pass muster with any standard of modern democracy, but the collapse of most of the Italian republics in the face of internal conflicts and the seemingly superior power of the princely powers was again held up as evidence that democracies couldn’t work. 

Indeed, a lot of the Enlightenment’s intellectual work, from Montesquieu to Rousseau to the Federalist Papers to Tom Paine, was about trying to construct a working theory of democracy in the face of pretty loud arguments that the whole thing could never work.