The skimmer is designed to do exactly that - skim debris off the surface BEFORE it gets a chance to sink to the bottom. Some debris will still get into the pond, but the skimmer does help. As far as the surface water being "cleaner" - I think you'll find that a waterfall at the opposite end does a good job of mixing the water that's been through the filter with the rest of the pond.
You'll get mixed reviews on skimmers. I personally think a skimmer gives a pond surface a nice sparkle because it also removes the dust, pollen and other microscopic debris that collects on the surface by keeping it moving to the skimmer. And if you have trees around the pond, be prepared to do frequent scooping to keep the leaves out. The flip side is that you do have to clean the skimmer basket and the frequency of that task will depend on the amount of debris you get in the pond. And people do find that fish or frogs or other small creatures can get caught up in a skimmer.
So I guess it's really a matter of personal choice. We built our pond with a negative edge so we get the skimming action without the upkeep of a skimmer.