No, the P1800 was by Frua whilst they were part of Ghia and it doesn't look much like the puzzle drawing.
I would say the puzzle is by Vignale as you can see all their trademark features llike the recessed tail-lights, in vogue with Vignale at the time, but whilst there are a number of Vignale prototypes that resemble the drawing I haven't found any that are the same.
The Vignale Volvo Elisabeths looked like this, but neither are the same as the puzzle drawing: