Yes, it could have, but it could have been even worse. Some of the worst responses to the pandemic worldwide have come from authoritarian regimes, which have apparently put more stock in denying that such a problem exists than actually fixing the problem.
China was somewhat of an outlier in that it’s an authoritarian society that actually did manage the pandemic well for the most part - it went to extremes to do so, in fact. More often than not, though, in democratic societies, there’s inherently greater accountability when political systems fail at something. One of the reasons the US has failed to respond well is that many of the leaders in this country responsible for mounting a response to COVID are themselves authoritarian
That being said, democracies function only as well as the quality of their collective analysis, decision making, and behavior will enable them to. My general prediction is that the world as a whole is about to enter a period of markedly less freedom, and it will have a lot to do with climate change, and how climate change reshapes politics and even political boundaries. Climate change is going to place unbearable stress on political systems, both democratic and undemocratic ones. But the appeal of the ones that are less democratic is that they will have greater political efficiency.