Add icon to a category

In theory, yes, but it’s not something that will just work out of the box, you’ll need to dust off your coders hat.

Off the top of my head, upload your icons and then modify the calendar.php code to take into account what you want to do; at the moment the hex colour is stored and added in as inline style. You’d want to change that so that some class was referenced instead based on category and then use the CSS box on the calendar options page to define that CSS code.