A Normal Map only has information about the direction the Normals (vectors, perpendicular to the surface) are facing, not how far a Vertex is displaced. That is totally different information and neither can be used as a substitute for the other.
However, I did manage to get some result;
I appended the Head in 3.3 and used Kent’s trick to rebuild the Subdivisions and then was able to Bake a 4096 x 4096 (32 Bit) Texture:

Some problems: the level 0 head is not the same as the original (because the Rebuild only ‘un-subdivides’), but that shouldn’t really be an issue. The other thing is, that some Multires Data got corrupted and needs to be fixed (exploding Verts) from Level 1 up to Level 6, one after the other.. And you lost your Shapekeys (had to delete them, in order to be able to Apply the Multires).
As you can see, I also made a mistake, when Saving the Image, I used Half Float Precision, with the 32 bit texture, it is better to Save it as Full Float.
But all in all, I think it’s at least a partial success.