It comes down to a DM ruling
Unfortunately, the rules aren't 100% clear on the issue of when exactly a reaction occurs, and Jeremy Crawford/Mike Mearls both seem to leave it to DM ruling for other reactions. (note that Crawford says "I have it happen after" as opposed to speaking in a rules-authoritative voice). The PHB errata also does not clear up this issue.
However, one reaction that occurs on being hit with an attack and that could potentially negate the attack is the Shield spell. Notably, it specifies that the +5 AC added can negate the triggering attack, and functions against other attacks until the start of your next turn.
Given that shield specifically calls this out, and other reactions-to-hit like Wrath of the Storm don't, you might infer that the hit generally takes place unless some specific rule negates it, and there is no specification in Wrath of the Storm. Other effects that can negate attacks like the Protection fighting style use the word "attack" instead of "hit". So in this case, you still get hit by the attack and suffer any consequences of the attack. Those consequences include taking damage and not being able to take reactions. Then the Wrath of the Storm reaction trigger occurs (being hit with an attack), but you can't use it. This effectively eliminates a corner case where, otherwise, you would get hit, but Wrath of the Storm kills the target before you take damage/suffer effects of the attack.
However, a DM may still rule otherwise, and it would be difficult to make a RAW argument opposing it (provided your DM was interested in hearing such an argument in the first place).
Specific
The first question you need to ask is if the creative use of the spell agrees with the spell requirements.
PHB, p. 275:
Lightning springs from your hand to deliver a shock to a creature you try to touch
This spell requires you to deliver on a creature, and not an object.
Now, this doesn't really answer your general question about creative use of spells, but it does give guidance on the specific example you gave.
General
Generally, The Rule of Cool* should encourage creative solutions, as long as they fall within agreement of the rules. Ultimately, there is no real guidance as to how to handle this as DM other than 5e giving the DM ability to adjudicate decisions. You've got the freedom, you've got the power, just come up with something reasonable that is fun for everyone.
Also consider other effects someone's creative idea may have. They may want it to work one way, but if you see additional effects that could happen, then feel free to add them.
In the case of something like Shocking Grasp, instead of targeting the water (which is not a valid target), the player could target a creature who is in water and have the electrocution spread out out from your target to effect anything in the water (foes, friends, and possibly/probably self.)
It is a trope that essentially means a willing suspension of disbelief for the sake of a cool moment... In RPGs, this generally refers to occasionally allowing the chance for ridiculous stunts or unique interpretations of the some of the rules or features of a system for a possibly cool moment.
- In an RPG, the Rule of Cool means giving your players the chance to perform ridiculous stunts or bend the rules a little bit in the sake of an awesome scene.
- Be warned, you should establish the level of craziness your game will allow early on to play with people’s expectations.
- Apply the Rule of Cool sparingly—that goes for the GM just as much as the players! Too much gonzo action will turn your A Song of Ice and Fire RPG into a Dragon Ball Z game faster than you can say “Super Saiyan.”
- Gauge which player actions are viable, and which are abuse. This is more art than science, but you should reward creativity while dissuading players from reaching too far too often.
- And don’t forget: most RPGs are designed to tell stories of epic fantasy! Never say never—there’s always the chance someone rolls a natural 20!
Best Answer
When going for RAW
The stat block of Animated Armor shows next to his Armor Class that he has natural armor, thus he does not count as wearing armor made of metal.
It makes sense
The advantage from Shocking Grasp against targets wearing armor made of metal does not increase the damage, but the hit probability.
When fighting a living person, you have to aim for his body. When attacking him with lightning his armor is also a valid target, which makes it easier to hit him. (-> Advantage)
When fighting an Animated Armor you actually have to hit the Armor, there is no benefit in it conducting electricity.