The back cover itself does have an impact on reception, as it acts as a ground plane for the motherboard. I have seen iPhone 4's and 4S' alike with serious reception issues simply from not having a good back cover properly installed. It is not common, most of the time the phone should work normally with no back cover on it whatsoever, but I just wanted to mention that it is a possibility.
Also if you have access to a microscope and multimeter, check continuity of the inductors (small rectangular 2-pin component that is essential a piece of plastic wrapped in wire) near the antenna connector. If one were knocked loose due to impact, it will also cause this issue.