I really don't think so. I remember looking at the screen after I installed it and thinking that it looked great except for one spec of dust on the screen and one spec just off the screen. Now I have several specs on the screen and they were not there before.
Most likely there the whole time. I've noticed depending on lighting conditions you will not notice dust under the protector after installing. In certain lighting conditions you might notice dust that wasn't noticeable in a different setting, but it's safe to say it's always been there. And once your eyes catch that dust underneath, you'll begin to always see it.
If it's a static protector, i suggest run a little hot water in your tub in the bathroom so it gets a tad steamy (to keep dust from swirling in the air), then take some scotch tape, lift the edge closest to the dust, take a toothpick and try to snag the dust and remove. also, it goes without saying, don't do this anywhere near your tub/shower that might be wet.