Yes, Java Beans can definitely have behavior. Java Bean classes without additional methods have very limited applicability, because they encapsulate data devoid of useful behavior.
Oracle mentions this in one of their tutorials on Java Beans:
A bean's methods are the things it can do. Any public method that is not part of a property definition is a bean method. When you use a bean in the context of a builder tool like NetBeans, you can use a bean's methods as part of your application. For example, you could wire a button press to call one of your bean's methods.