Now creating a tag family it's possible to place a label and turn off the "Visible" option for it. After loading the tag family to the project there isn't any signs that the label exist inside the tag.
In Autocad I created attributes and placed its on DEFPOINTS layer. And I could see non printable parameters and manage my drawing.
So in Revit will be nice to see "Invisible" labels when the tag is selected, as we can see Temporary Dimensions of selected element. Also it makes possible to change labeled non printable parameter as a usual label in a tag. It could be the easiest and fastest way to change the most frequently used object's properties against to seek desired string in long list of Properties dialog window.