Could you drain a battery with only one terminal connection?
- "A current must always return to its source"
This statement is a simplification, which ignores the category of phenomena we call “electrostatic”. It would be better to say that a continuous current must return to its source.
Current is the flow of charges. Therefore, any current that does not flow in a complete loop ("return to its source") must be either increasing or reducing a charge imbalance (also known as a static charge), where some portion of the system contains more electrons than protons or vice versa.
As a charge imbalance increases, the electric field opposing it increases. Thus, eventually whatever process is causing the imbalance will not be able to increase the charge imbalance further, or something else will happen (such as an arc).
A typical example of a process which increases charge imbalance is an electrostatic generator such as a Van de Graaf generator, or rubbing your shoes on carpet — but it is also the case if you touch a piece of metal to one side of a battery, a current will flow momentarily and the piece of metal will be charged. But it'll only flow until the piece of metal is charged to at most the battery voltage, so this will not discharge the battery significantly. (And that much static charge is extremely hard to notice, because familiar electrostatic phenomena like static shocks involve hundreds of volts, and attempting to measure it with any conventional voltmeter will quickly discharge it.)
In order to get a continuing discharge of the battery, you need to do this repeatedly. And getting the current flow to happen repeatedly means you need to discharge this hypothetical piece of metal, relative to the battery terminal — which means you need to connect it to the other terminal of the battery. Thus, there is still a loop of sorts — it is just oddly intermittent.
A famous machine operating in this fashion is the Oxford Electric Bell, a specific variation of Franklin bells, which consists of a pendulum (the “clapper”) hung between two electrodes (the bells) that are connected to a battery. The clapper touches the bells alternately, and each time it does this some electrons enter or leave it to equalize the charge between the clapper and that bell. Electrostatic attraction causes the clapper to swing between the two bells on its own, keeping the machine running. Because the amount of charge (and energy) transferred is so small, it has been operating with its original battery for over a hundred years.
(You can build your own Franklin bells out of common materials. Unfortunately the suggested safe source of high voltage, the face of a CRT television, is no longer a common household item. You might be able to get it to work a little bit with some carpet shuffling, though.)
So, it is entirely possible to discharge a battery by connecting to only one terminal at a time, but not only one terminal ever; any system in which only one terminal of a battery is connected will enter a steady state which does not discharge it.