There is no 'jquery' type of selector in scryber, and the Visible property is not style based (I know - but we use it well before the styles are built).
However, one thing you can look at is setting the style definition that should be applied dynamically rather than the property.
If your div is assigned a class e.g.
<pdf:div style:class="existing-class hide-me" > My content to hide </pdf:div>
Then in the code generation, when required, you can create a new PDFStyleDefinition for 'hide-me' and position the divs off the page content.
PDFStyleDefn hidden = new PDFStyleDefn();
hidden.PositionMode = Scryber.Drawing.PositionMode.Absolute;
hidden.Overflow.Action = Scryber.Drawing.OverflowAction.Truncate;
hidden.Position.X = 5000; //Enough to move it off the page
This should work