It can, with one in the pipe and the hammer down.
You will be hard pressed to do so without installing miss fitted parts. When the hammer is down and resting on the firing pin, the firing pin does not rest on the primer of a chambered round as it is too short to protrude past the breech face. Further, the firing pin is held to the rear, away from the primer by a spring. Unless the hammer strikes the firing pin with enough energy to overcome the spring and inertia, the pistol will not fire. Such energy can not be developed when the hammer is at rest on the firing pin stop. In short, dropping won't discharge the 1911 pistol when the hammer is down.