Yes and no. It really depends on the quality of the program's resize algorithm. On a good program like photoshop (or others), you would be hard pressed to notice any visible loss. In fact, on a shot that isn't very sharp, resizing down can sometimes mask the problem. On the flipside, if you use a basic program like MS paint to resize a photo, you will notice the introduction of blocky artifacts. It's all about the quality of the interpolation algorithm.