Can I use one alkaline battery to recharge another? Unfortunately, I don't have batteries to waste to test this myself, but I am curious... 

Let's say you have two identical batteries. AA Duracell.

Now let's say you run one of the batteries through an LED until the LED starts emitting at half the intensity it was emitting at when you first started (effectively draining the battery to half voltage)

Now, lets' say you touched the positive ends of both batteries for a reasonable amount of time, and then did the same for the negative ends.

Given that the used battery would have a much lower voltage, raw electrical current would travel from the unused battery into the used battery.

So this brings me to my question -- Would the batteries now effectively have the same amount of energy in them? I am not just talking voltage, but chemically too, or would the similarity in voltage on both batteries immediately disappear if either of them were used (because while, yes, either end of the battery does contain equal electrical charge to its counterpart, either end of each battery does NOT contain equal chemical potential)

To simplify this, would touching two batteries as described above effectively drain the unused one, and charge the used one?
First, some batteries are rechargeable, but some are not. However, even if we talk about rechargeable one, then
1) some degradation during recharge usually occurs
2) deep equality will require very long time to achieve