I would like to put an object (be it a div or img or text) that is visible when the pdf is shawn on screen, but that is not printable.

The same way as you can do when you define an interactive button in InDesign (unchecking Button in Printable) or when you, inside Acrobat Pro, say that a layer of the pdf is visible but not printable.

Thanks

We don't yet have a way to do this with Prince. We will try to add it in a future release.

Is this already possible? I couldn't find anything in the documentation.

No, this will require support for PDF forms or something similar.