Of course you can be Fat & Fab! There are a lot of examples on YLF & otherwise on the blogosphere. www.garnerstyle.blogspot.com comes to my mind at this moment!
For me, looking curvy and yet sleek and structured at the same time is a style goal. I need a lot of structure in my outfit and I haven't taken on to the fluid fits in vogue very whole-heartedly tbh. My style for me means fitted clothes - skinny jeans etc as well as creating columns of color. That does make me look sleeker and I do feel fab in that as well!

No, I feel Fab when I am happy with the elements of my outfit , the way they compliment each other and most importantly when they FEEL Fab.

I think the vast majority of women have some degree of body image issues (myself included) so I completely understand where you're coming from. I don't only feel fab when an outfit makes me look thin, though. I have outfit elements that do exactly the opposite (harem pants and/or oversized sweaters/sweatshirts do exactly the opposite on my small frame) but I feel comfortable AND fab wearing them depending on how and what I've styled them with that make the outfit feel "me." That's where my happiness factor comes from. You could probably put a pretty, frilly and totally figure flattering form-fitting ensemble on me that may make me look ultra skinny and taller --but the fact is I'd feel pretty crappy wearing it because it wouldn't feel like it was "me" and it would be uncomfortable, which would make me want to fuss with it. I'd spend the entire time wearing it feeling rather self conscious and awkward, no matter how much it might make me look thin.