I think this could be programmed as a plugin using the standard API. I'm not saying this would be easy, but I'm sure it can be done.

Here some tips:
a) The monitoring of furniture properties like name and elevation can be monitored by attaching listeners.
b) From a graphical point of view you need only basic elements, i.e. the polyline and the label.
c) The label and polyline can be logically linked to a furniture using the custom properties.
d) The label position relative to the furniture can be saved using custom properties.
e) as a furniture moves the polyline and label position can be changed accordingly using a listener (as at point A).

If you look at the "Link selected furniture" feature from the Wirings plugin you can get an idea of how it cloud be done in a plugin. Watch the last part of the following video, you will see polylines that follow a furniture:
https://youtu.be/Z_XFq4QaD8E