No, that's not possible with Inkscape.
You can simulate such a feature though. Using Snapping (Snap nodes and handles, snap cusp nodes and/or snap smooth nodes) you can position the nodes directly on top of each other. Then using the Node tool, select them by the so-called rubberband or selection box technique, i.e. draw a selection box around the "stack" of nodes. Then when you move the top node, all of them move with it.
Oops, hi ~suv! You sneaked in your post while I was typing mine