No, those boots you saw are not dress boots. They are cheapo "dress boots" which are essentially field boots without laces. There is no stiffener, and no whale bone. Therefore they are not truly dress boots.
A dress boot will come in various hardness, and will have a whale bone (now made of plastic) up the back of the boot so the boot keeps its shape and forces the leg to conform to it, and stay in a certain position. Konig is one of the most well known brands, and the most popular. So yes, it will stabilize the ankle far more than a flimsy field boot. Compare it to wearing socks versus steel toed boots with ankle support. A dress boot also will not drop down that much because of the stiffner, and the break in time is less. As well one should not walk around in or soak a dress boot to break it in as this will wreck the boot. Dress boots are for riding. Not walking around.
They say money doesn't buy happiness -- well happiness doesn't buy horses!