That's the interpretation that makes sense, yes.
Since there is no demarcation between fluff and crunch in spells, the whole spell effect is rules. The effect says that it lessens the effect of the triggering damage; when you wonder "how?", the effect supplies the answer: you have resistance.
D&D 5e is somewhat resistant to fine-grained timing analyses, and doesn't appear to try to nail down a precise tick-by-tick ordering to things that could be resolved simply by the DM saying, "Yes, it does what it says on the tin." Since any other interpretation makes the spell not do what its effect says it does, the interpretation that lacks internal contradiction is the correct one.
If it helps, Jeremy Crawford has tweeted about this, once:
Q: Does Absorb Elements give you resistance to damage from the triggering attack?
A: Yes.
And twice:
Q: When someone casts Absorb Elements, does he take full damage from the attack he is reacting to?
A: The absorb elements spell works against the spell that triggers it.
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).
Best Answer
Correct, you cannot cast absorb elements in response to shocking grasp
Reactions happen after their triggers unless specified otherwise. The trigger for absorb elements is taking damage...
...but when you take damage from shocking grasp, you can't cast reactions anymore:
This means that you never have the opportunity to cast absorb elements, as you correctly deduced.
This is different from shield because shield triggers when you are hit or counterspell which triggers when the spell is cast while absorb elements triggers when you take damage. You aren't reaction-blocked until after the hit, and shield can intercede in that hit.