I will leave the debate over whether or not you should ever do this to others, but thanks to a post by Joshua Kohl in the AUGI Revit® Architecture - General Forum, I now know how to create a dimension with absolutely no dimension value or other text showing. You may be aware that while you can override the dimension value with text, by double-clicking on the dimension text to open the Dimension Text dialog,
Revit will not allow you to enter a string that consists only of one or more Space characters here. But if you right click, a context menu will appear, and you can choose the Insert Unicode control character flyout, and then the Unit Separator (Segment separator) character.
The net result is a dimension string without any text.