Yes it does.
In a democracy, the notion, ideal though it is, is that citizens have an equal stake in the governance of a polity. In modern democratic polities this is reflected in such institutions as universal suffrage, or that one is equal before the law or the possibility of being elected to the main governing body, or even leading it. And other institutions such as universal education, healthcare and welfare.
This is very different from its direct opposite, a monarchy where such institutions were, for obvious reasons, not tolerated (though they might have magistracies of various kinds representing the nobility and welfare for the same class).
It’s worth noting here Plato’s The Republic, which served as a philosophical blue-print for theorising about the nature of republics and of polities in general. For example, St. Augustine compared the city of men to the city of God.
It’s also worth recalling, that before liberal democracy broke out into the open in modern Europe (and pushed the ancien regime into history or at least irrelvance), it was preceded by the Enlightenment, part of which involved the recovery of the Greek philosophical tradition (and which had already played a substantial role in Islamic civilisation and in fact has mediated its recovery in Europe by Ibn Sina (Avicenna) and Ibn Rush’d (Averroes).
It’s worth adding, I think, a few points that J. S. Mill made on his essay on Tocquevilles Democracy in America here:
It is necessary to observe that, by Democracy, M. de Toqueville, does not, in general, mean any particular form of government. He can conceive a Democracy under an absolute monarch.
Nay, he entertains no small dread, lest, in some countries, it should actually appear in that form. By Democracy, M. de Tocqueville understands equality of conditions; the absence of all aristocracy, whether constituted by political privileges, or by superiority in individual importance and social power. It is towards Democracy in this sense, towards equality between man and man, that he conceives society to be irresistibly tending ...
For, in democratic institutions, M. de Tocqueville sees not an aggravation but a corrective of the most serious evils incident to a democratic state of society. No one is more opposed as he is to that species of democratic radicalism which would admit at once to the highest of political franchises, untaught masses [which is one reason for the emphasis Plato put on education in The Republic] who have not yet been experimentally proved fit even for the lowest.
But the ever increasing intervention of the people, and of all classes of the people, in their own affairs, he regards as a cardinal maxim in the modern art of government; and he believes, that the nations of civilised Europe, though not all equally advanced, are all advancing, towards a condition in which there will be no distinction of political rights, no great or small very permanent distinctions of hereditory wealth; when as there will remain no classes nor individuals capable of making head against the government - unless all are, and are fit to be alike citizens - all will, erelong, be equally slaves.
And this from an aristocrat!