Yes indeed. I’m guessing from your previous activity on the forum you are comfortable with (and probably have already set up) a custom event-form.php template but just let me know if you need help with that.
What we’re going to do is look for this line of code and replace it with this code instead.
Note that one side effect of this approach is that only one category can be selected by the person submitting the event (whereas checkboxes allow them to select multiple categories), however that may be a positive thing depending on your requirements.