In theory, plugging both of them into the same circuit (such as two plugs in one receptacle) shouldn't damage anything as far as I know. Of course, it won't do anything useful, and if the plug is not polarized then there's a good chance of plugging it in backwards and shorting out the circuit.

And, as you learned then, there is a great danger of accidentally touching the live end. "Proper" use of this, if there is such a thing, would dictate plugging the load in first, then the supply, but in this case there was supply on both ends.