Answer:
It does teach us some things, especially when it comes to things such as quarantines, economic effects, and societal changes. However, the Black Plague was a much worse pandemic that actually killed over a third of the European population at the time. For this reason, the scale of the events and its consequences is a lot different, and difficult to compare with the current situation.
For example, the Black Plague actually led to radical changes in the European feudal economy, because so many people died that lots of land became vacant, or had less farmers available to work on it, a population decline that caused farmers income to rise substantially, due to scarcity of labor.