Of course. A manufacturer designs a printer to produce a certain level of repeatability for any given RGB triplet. They just don't much care about forcing it to a specific value when color management is disabled. It can and does vary with printers and even different paper settings on the same printer.
So let's run with that. Let's say that my specific printer/paper settings combo was preprogrammed to lay down 50 units of ink for every 128,128,128 pixel (with CM off).
Now we feed the printer a sheet of EEF and let Colormunki do its thing. (Actually, two sheets because ColoMunki makes two passes.)
After that is said and done, we now have an ICC profile.
Now let's print out my ProphotoRGB 11-step target with CM turned ON and the above ICC profile selected. For simplicity sake, let's just print out the zone V patch, the one with an eyedropper value of RGB 128,128,128 and LAB 61.
If we could examine this print under a microscope, we would no doubt see that the printer did not lay down 50 units of ink like it did when CM was turned off. On the contrary, the actual number would be greater or fewer than 50 units due to the influence of the ICC profile. Let's say, for the sake of argument, that the ICC profile caused the printer to lay down 40 units of ink instead of 50. Why 40 units, you ask? Because that's how many units of black ink it took to satisfy the Colormunki. The Colormunki wants middle gray to render a certain way and, by God, it will see it through.
What I want to know is what does the Colormunki think 128,128,128 should look like? It must have its own definition of middle gray preprogrammed into it by the manufacturer. And this definition of middle gray must be in units of L*a*b because that's how the Colormunki spectrophotometer see things--in L*a*b.
It is the nature of this internal preprogrammed definition of middle gray as it exists in the eye of the Colormunki that lies at the heart of my inquiry.
Or is the rabbit hole getting too deep?