I don’t know how to insert a drawing into the writer. I have a curved connector which leaves and returns to the same object, a circle. When I copy and paste, the curved connectors are converted to ellipses with going through the object. I don’t see an import to import a draw.
This is one of several inconsistencies with Writer/Draw. It looks like Writer takes the drawing description and recomputes object placement and routing. Look for similar questions.
If you don’t mind low-resolution images in Writer, try Edit>Paste Special... for various formats.