To me, it seems to be on the same formality scale as sweater + pants + shoes, which constitutes the majority of this thread.
As to whether it fits into a casual classic menswear cannon, I don't know. What I will say is that I do read a lot of Will's stuff on asuitablewardrobe and other CM sources, and that helps me to put coherent combinations together. I draw a lot of inspiration from proponents of classic menswear, but I don't want the outcome to look classic or preppy or trad or anything like that.
I think you could make an argument for each element, but the combination and the application take the whole out of bounds.