You may run into conflicts. This will be very obvious if you use bubbles or listen to both events on the same object. Essentially, event listeners listen on a string. There is no strong typing, just checking if (string == type) (this is simpler, but essentially what happens).
:
public static const EVENT_TYPE_ONE:String = "eventTypeOne";
[Event(name="eventTypeOne", type="com.me.events.CustomEvent")], .