Yeah, definitely Arty. Although I think there is a place for drape in most style personas. (Maybe not true Sporty types, I guess...). It could also go boho very easily, or urban (if you go for more architectural, angular drape). And you could of course combine it with classic pieces as has already been mentioned.
So... how you implement it is up to you. Personally, I do need to add a little structure and some sharp lines, otherwise I feel too soft and round. This has a bit to do with my body type though, as I am pear shaped with a roundish shoulder line. So, I prefer things with some structure at the shoulder because I don't like to accentuate the rounded shoulders or my slouch. I also often like to show some leg, either in a skinny pant or shorter hemlines, when I'm wearing something very drapey. I have a long leg line so I find this pretty easy to accomplish. I also have straight hair with a sharply angled cut, which helps keep things from becoming too soft as well.
By the way, I have the KUT jacket you linked above. I think it's a great combo of drape and structure, and I'd recommend you give it a try while it's still on NAS discount.