Has the Church ever endorsed universal suffrage?
The Church does not endorse any particular form of government (in particular, the forms of government enumerated by the ancients and considered by the medievals -- monarchy, aristocracy, or polity). It only requires that government serve the common good (rather than the private good of those who are ruling).
A quick search reminded me of this post at Ite ad Thomam. Talking about who is qualified to participate in ruling and who is not is implicitly tied to claims about distributive justice. I don't see the Magisterium coming out with a statement supporting [absolute] universal suffrage (which ignores the question of whether one is morally qualified to rule or not) when this would be contrary to distributive justice. (Individual bishops and priests may do so, but I would claim that they do not have adequate support from Tradition or reason. Praise of liberal democracy exists, even at the highest levels, but it is, as far as I remember, limited and conditional.)
Still, even if the Church hasn't endorsed universal suffrage, it may maintain that that in communities where it exists, Catholic citizens have a duty to exercise citizenship (to participate in elections and so on). Power should be used if it is given to one, even if he does not deserve it, for not using would be failing to prevent others from misusing it? However, what if he cannot exercise it well? What if Catholic citizens perceive that they are not qualified to vote, because they are not well informed of the issues or candidates? Not only can they opt out of voting, but would it be morally necessary for them to do so?
What of the apparent paradox that the knowledge that one is not qualified is founded upon the knowledge of what is necessary to be qualified, and those who have this fundamental knowledge are thereby qualified? We would have to break this down and look at what is actually known and to see if it is the same in all three cases. In the first, one may have opinion or moral science of who should be a citizen, but the most important qualification of a citizen is his virtue: the moral virtues including prudence or practical wisdom, which are not identical with opinion and moral science.