Technically, a slim person can wear almost any style of cut given he is evenly shaped. By that I mean that none of his body sections (shoulders, chest, waist and hips) is far out of proportion.
The actual A&S cut that I have seen on the website and the BBC series let me to believe that it works well for the slimmer customer. This is supported by the pictures of some of the finished garments on their site. The pattern runs relatively straight up without turning too much towards the neck.
Even the overcut shoulder will work well unless exaggerated and will give the wearer a "sporty" appearance.
With a portly figure the problems start. When visited by Ozwald Boateng John Hitchcock explained that A&S cut a wider shoulder to make the waist look slimmer. But this works only well up to a certain amount of waist girth.
The main problem is the (vintage) cutting system they use, which has a neck point that is rather far away from the neck. For a portly person the cutter will have to add width at the front waist line to accommodate for the fullness of the belly, so the neck point will be even further away from the neck.
To get the neck hole of the coat close to the neck of the customer tailors can either manipulate the pattern or the front part (cloth). The usual procedure is to shrink the front along the line which will later become the lapel fold line.
By doing so the run of the pattern will be distorted and will create a sort of barrel like appearance (like in FNB's picture).
One trick is to give even the portly man a tapered waist above the waist. This will have a visually slimming effect when viewed from behind or front.
This is a coat I made a while back and it sits on a dummy that is a bit bigger, don't know the actual size, it might even exceed the portly range. First the lateral view (Btw, the balance is off due to the dummy):
Now the front view:
(And yes, those are a machined lapels...
Note the taper from the armholes down to the waist.
I'm not sure if this can be done for a portly figure without a side panel in a satisfying way.
Better and more knowledgeable tailors may correct me.
In my coat is no front dart, so there is no wedge as well, just a side panel. Makes the pattern matching a bit easier.
There are drafts without a side panel with a cut from the front dart down to the hem which is then pinched, but that will throw the pattern out of the grain line.
I'm not sure which method is used at A&S right now. Should depend on the cutter and the customers figure. My preference would be a separate side panel (with a wedge for the really belly shaped guys)!
Here is a portly guy in an English Cut coat:
Needless to say that I'm not very fond of the look of it...