How to control the visibility of an object by means of visual style? Is this possible?
Do you mean, for instance, that you wish to make an element visible in a Wireframe View but not visible when the View is changed to Shaded? If so, that is not possible. What exactly are you aiming to achieve? Perhaps there is another way to accomplish this.
The best you can do is to set up the model elements and the nested annotation symbol to be visible/invisible under the specified Detail Levels. In the Family Editor, you can select one or more objects (including nested Families) and under Properties, you will see "Visibility/Graphics Overrides". Click "Edit..." and then following dialog will allow you to define under which Detail Levels the selected object will display.