The only element that is visible but non-printing in ARCHICAD is the Hotspot. Useful for placing critical snap points. Various on-screen options (e.g. section depths) are non-printing as well.
If you want arbitrary geometry to be visible but non-printing, your only options are to us a layer that is visible in an 'editing' model view, but turned off in the model view that a placed drawing is based on...
or... you can use Trace & Reference and reference a view that shows the layer(s) that hold things that you do not want to print - while the main view describes the printable view. Since a reference can be to the same or another story, a worksheet, etc you have choices beyond layers as to where to place the non-printing information.
Layers is the easiest solution; not sure why you don't want to do that?
One of the forum moderators
AC 28 USA and earlier • macOS Sonoma 14.7.1, MacBook Pro M2 Max 12CPU/30GPU cores, 32GB