Yes, you can add an event and display it in more than one category.

To do this, turn on the "Mirror Category" option via:

Admin Menu > Calendar Settings section > Calendar Options > Under "View Controls" > "Check to enable event mirror categories" > Save

When adding an event to more than one category, you must use the Full Event editor pictured below.  Click to add event then click [More event options...] button.  Quick Event does not support mirror categories at this time.
 

Important Note:  you must assign a primary "Category" and you may assign one or more "Category Mirrors" using the category drop down selectors. The primary category selected will determine the event's viewing permissions and category default font styles.

All calendar views and website plugins will now display an event if a permitted primary category or mirror category is selected.