Sure it does! If news happens, or anything to make people start buying the stock, of course the shorts will want to come out ( or they lose money as the price goes up). So the covering simply adds fuel to the fire as a short cover is simply a buy ( same as a regular long buy). Imagine a large volume day of upward movement, people, institutiions wanting in, then add on several million (legally shorted shares)of buying on top of that for short covering. Not to mention the naked shorts covering also, and I'm not sure if that number can be determined.
That's why we get such an explosion when there is really good news out.