I had a three-piece lefort I where my upper arch was expanded and moved forward very slightly (~1mm), and it did change my nose shape. My nose tilts up slightly more now and the bottom of my nose has widened a little bit. This combination makes my nostrils a lot more prominent now. Even though almost nobody noticed, it still bothered me for a while, but I'm getting used to it.
I think in general, an upper jaw advancement won't make your nose any bigger, but it will upturn your nose and widen it slightly at the bottom. The widening can be minimized using a special suture called an alar cinch, where a suture is put through the edges of your nostrils and then pulled together under your face.