The alcohol does affect the reading of your FG, what you are measuring is Apparent Attenuation, which gives you a rough but not exact measure of how much alcohol is in your beer, when compared with your OG. It doesn't tell you exactly how much alcohol is in the beer, but its pretty darn close, and I think more precise ABV measurements would require a lab with some fancy equipment.
Its also useful to know when your fermentation has stopped. Once the gravity levels out for a few days you know fermentation is complete and your ready to bottle or keg your beer.
EDIT!!!: Im an Idiot, I thought I read Hydrometer. My refractometer is a frustrating piece of equipment and i rarely use it. Forget everything I just said