Fredrik, the Back Focal Length does not tell you the Diameter of the Front Lens. The Back Focal Length is related to the curvature of the last Inner Lens. The Diameter of the Front Lens is directly related to the Pupil Diameter referred to in the quote. I've called the "pupil" the Aperture, and perhaps I've confused you by using the term "Aperture".
mts, did I explain this correctly?
I'm not mts, obviously

, but will answer that: over all, no.
The diameter of the front glass can set a limit to the amount of light a lens 'gathers', yes.
But (simplifying) the amount that a lens let's through is set by the diameter of the entrance pupil that was mentioned before.
The f-number (which is the measure for how much light a lens lets through) is directly related to the diameter of the entrance pupil and the focal length.
And that is an important thingy: my f/4 40 mm lens has a much larger (2x) diameter front lens than my f/2.8 80 mm lens. So the lens with the smaller diameter front lens lets more light through.
My f/2.8 50 mm lens however has a front lens that is about equal in size as that of the f/4 40 mm. Yet they do not both let pass the same amount of light.
The diameter of the front lenses of my f/2.8 150 mm and f/2 110 mm lenses also are about equal in size. And again, not equally bright.
So obviously the diameter of the front lens is not all important.
Now look at the pupil diameters: the diameter of the entrance pupil of the 40 mm lens is 10 mm, that of the 80 mm lens is 29 mm.
Divide 40 by 10, 80 by 29, and you'll get the f-numbers.
The differences in lens speed between the other lenses mentioned also reveal themselves when you look at the diameters of their entrance pupils and relate those to the focal length.
So the diameter of the front lens is not (!) directly related to the diameter of the entrance pupil.
It's a bit more complicated.
The purpose of large diameters in astronomical telescopes is not to increase the light gathering power, but to increase the resolution.
The larger the light gathering surface, the smaller the distance between two objects can be while still being seen as two distinct objects.
Or rather: the greater the maximum distance between the light gathering 'bits', the greater the resolution. You can combine small telescopes, creating a 'diameter' much larger than would be possible if only a single telescope had to be used. The greater the distance between the two, etc.
Such an array does not do much to increase the amount of light gathered, but it performs small miracles for the 'quality' of the light.
"Back focal length" is really a wrong term to use. I like "back focus" a bit more, but the German term "Schnittweite" a lot better. "Schnittweite" obviously contains no reference to focal lengths, and thus avoids confusion.
It's too easy to confuse the distance between last lens element and film plane (which is what is meant by the term) with the focal length, when the term for the first also contains the words "focal length".
The rear focal length (= the distance between the rear principal plane of a complex lens and the image plane when the lens is set to infinity) can be much greater than the "Schnittweite" (in telephoto constructions), or much smaller than the "Schnittweite" (retrofocus constructions).
In (near) symmetrical lenses, the rear focal length is a bit larger than the "Schnittweite", the difference being about half the distance between first and last lens surface.
So in a complex lens (or even a simple, but thick lens), the rear focal length and the distance between the last lens and film plane never are the same.
So why use the words "focal length" in a term to describe the "Schnittweite"?