The
short answer is that two bats can no more become one than a
broken bat can heal itself.
Rather than work with a baseball bat, let's conduct this little thought experiment. Imagine a slender stick of wood, perhaps something you might find on the ground after a windstorm. Pick it up and holding it by each end, give it a tug. Experience tells us that the stick is going to resist our efforts to pull it apart along its long axis. Now bend the stick until it breaks and immediately shove the two parts back together. A repeat of our pulling exercise will show you that something fundamentally irreversible happened when the stick was broken.
The molecular bonding that held the stick together so strongly when it was one piece requires that the molecules be in intimate contact. When the stick was broken all the bonds along the break were destroyed. This left a lot of unsatisfied molecules looking for ways to achieve a full outer shell of electrons or snapping up any oppositely charged particles that were available. Molecules are like some people to this extent. When they are not near the one they love, they love the one they are near. Oxygen molecules from the air, bits of dust, salt from sea spray... any old thing will be attached to the newly exposed surface to lower the high energy configuration resulting from all the broken bonds. This all happens faster than the speed of thought so by the time we can push the newly broken surfaces back together, they have accumulated an appalling collection of junk, preventing the original molecular bonds from reforming. What was one, has become two and as the saying goes, "All the king's horses and all the king's men" could not put the thing back together again.
Under some very special circumstances, the idea about making one thing out of two by simply bringing them together seems to work. There are experiments being designed for the near perfect vacuum of outer space. There if two metal objects are sufficiently clean and their surfaces smooth enough that good contact will be made, it is suspected that they will in fact bond together in a "cold weld". There is speculation that this may be one of the ways by which a space station might be constructed.