If you earth a piece of Natrium and drop it in water (salt and earth the water as well while you're at it). Will it still explode?
Yes.
You can perform this experiment yourself, on a much safer scale:
Obtain a piece of aluminum (any kind will do, as long as it's uncoated), and an alkaline solution (preferably NaOH or KOH in H2O; others won't be corrosive enough). For cathode, use something generic like steel or copper.
Insert the metals in solution (not touching), and observe the aluminum begins to bubble (hydrogen). Measure the voltage between the electrodes; should be something like 0.8V.
The [ideal] reduction potential of aluminum is actually something like 2V.
Short the electrodes together, and you should see some hydrogen from the cathode as well (this is due to the electrolysis current). Measure the current and you'll probably see something in the mA range -- it's a bad battery, but it does produce some power.
Now apply more than 2V (in the same polarity as measured). Ideally... this should stop, in fact reverse the reaction. But at most, you will simply cause more hydrogen to be produced (at the cathode), and not be able to prevent hydrogen production at the anode.
The reason is this: aluminum is so reactive that it is attacked by water, even when polarized with plenty of voltage. It is impossible to apply sufficient polarization to prevent attack, because the water itself will decompose above 1.2V or so. You simply can't get the necessary 2V at the metal-to-water interface -- try, and it tears itself apart. It doesn't matter whether this is applied to inert electrodes (like graphite or platinum) or by the force of a metal. It looks the same: the metal gives up electrons, with such force (electromotive force -- voltage) that the water is broken down in the process.
So, you might have an ideally 2V battery, but it only measures 1.2V (or less), and the remaining 0.8V is simply lost to heat, whether you're discharging the cell or not. So, the self-discharge is terrible, too. This is basically part of the reason why aluminum batteries aren't a thing, by the way...
You can react aluminum with an oxidant in an alternate solvent, and observe its reduction potential correctly; such solvents peak around 2.5 or 3V (something like propyl carbonate with a dissolved ionic salt), which is also necessary for lithium ion batteries, and also why ultracapacitors are rated for exactly 2.5V and little more: above this, the solvent breaks down, just as water breaks down beyond 1.2V. (You can build your own ultracapacitor, at home, using activated charcoal pads and salt water; it will have extremely high ESR because it's not optimized, and once again, 1.2V maximum before it stops working much like a capacitor. But the extreme capacity -- 10s to 1000s of farads -- is nonetheless sensible, as long as you take your time measuring it.)
Tim