I am not entirely sure why you are asking these questions, Asher. But since it is you, I feel that you deserve a longer answer.
First: it is not possible to emulate one medium with another. It never is. I sometimes visit exhibition of B&W pictures in museums and they often use inkjet prints for older negatives when they don't have a historical print and want to print big. So I can compare analogue and digital prints of museum quality. They are pretty close, but I can still spot which is which with the naked eye. And colour prints are so far apart that no museum I know exhibits one next to the other.
The mediums are visually different. Not better or worse, just different. The same is true for the whole reproduction chain: lenses of a certain type will impact a certain rendering to the picture, films have their own ways to render colour or grain, which is different of the one of electronic sensors and each printing technology gives slightly different results. Even paper surface will look different. Moreover, for reasons I have already sketched on this forum, the size of the sensor or film will directly influence the rendering of the lenses.
So, it is simply different. This is not the question.
What is the question?
If the question is: "how can I get the same effect as a given photograph?", the easy answer is "use the same devices". Some people do that and it is the main drive behind the revival of film. People see, for example, images taken with medium format cameras in the 50s or 70s, get a cheap used Hasseblad or Mamiya, shoot film and get something that indeed looks similar. Easy enough.
If the question is: "can I emulate the effect of a given photograph with a different process?", the answer is more complex. I'll take the example of Learoyds' image since this is what you gave us.
If the question is "can we emulate the original as printed on Cibachrome?", the answer is no. I am old enough to have actually used Cibachrome, I still have some prints somewhere and I know very well that Cibachrome looks like nothing else. If the question is: "can we get something close to that
small-resolution image above?", the answer is more complex. I would love to try. The image is deceptively simple. The light is extremely soft as in a painter's attic (if you remember the rooms with huge windows painters used at the turn of last centuries), although actually flash is used. The colour balance is generally cold and turns to excess magenta in the shades and mid-tones. That could be emulated with some effort in Photoshop. Highlights roll-off is peculiar (shoulder), that might be difficult to imitate. The depth of field, bokeh and general rendering of the lens is very soft and typical of large format, but medium format would probably come close. So we cannot emulate it exactly with digital, because we don't have a digital large format sensor and highlight roll-off is different with digital.
Could we emulate this with large format film? Well, you know more about large format cameras than I do, Asher, but I think that the main problem would be that no film has these exact colours.
But maybe the question was: "can we make a portrait that would be just as endearing as this one with a different camera?"
Here is a video where Richard Learoyd explains the process:
http://lectures.icp.edu/archive/videos/2011/Learoyd2011.html
Edit: I'll probably be criticised for that, but I made some calculations after having watched the video and learned a bit more about the prints. The results made me realise that we can't discuss these pictures without having actually seen the prints.
The prints are something like 180x120cm. Cibachrome has a very high resolution, the limitation is the lens. A conservative estimate of the result is about 1 gigapixels. Of course, most of the print is out of focus, since the depth of field is about 5mm, but still… the image must look sharper than life.
I can barely imagine what the models would feel. You are here, in front of the camera, and you know that the instant the flash pop, you will be imaged for display in a museum (or a collector's house) in eternity. And you'll the imaged just as you are: people can get a magnifier and count the pores on your skin. This is insane.