Could my battery break by dropping the phone?

Many things could happen inside a phone when you drop it, depending on how hard the concussion from the fall. The contacts inside could disconnect, the main board could crack thus breaking a internal wire in the sub-straight of the main board. Yes the battery could break depending on the angle of the shell of the phone and the surface that it struck, and the force that was applied. Even the contacts to the Sim Card could get mis-aligned so that the cell phone would not get a cell signal. Or even the antenna could break. Which is why many companies sell those plastic shells to protect the phones. Although they are made to protect the phones from falls they still cannot protect them from really long drops like if you dropped a phone from the Empire State Building or like the Eiffel Tower.