The docked Null's inventory overlays the inventory of Null you're holding. Distance did not seem to affect it - I went three chunks away and this still happened. However, it did not cross dimensional boundaries; if I was in the Nether while the docking station was in the Overworld, there was no flickering inventory. By shift-clicking on flickering items, I could pull them into my inventory as temporary phantom items, but they disappeared after a moment.

Video: https://vimeo.com/285677252