Not necessarily. But usually, yes. The smaller your pixel size, the lower "quality" your picture is.
Your 2 megapixel camera is only at best "quality" at the highest pixel size. If you do the math, the 1600 x 1200 works out to be a little less than 2 million pixels, which is how the name is derived. It means you have more pixels to display your picture, hence the quality change.