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.
Considering the below pages from the handbook sources I have, I have to say this sounds possible; though I didn't believe it at first.
Making an Attack: PHB pg 194
Choose a target: Pick a target from within your attack's range: A creature, an object, or location...
Resolve the Attack: You make an Attack Roll
First and foremost, you MUST make an attack roll. There are no sources to cite from either the PHB or the DMG that make exceptions to this rule. The recipient of any attack; melee weapon, ranged weapon, or spell attacks; does not have the option of getting hit without making the attacker roll first to get past armor class.
Now that we've dealt with that ... to make a melee attack you must choose 'A Creature within range' and since you are within your own range and count as a creature, you are a legal target for your own melee attack, unless the ability or spell says that you must target a HOSTILE creature. Making a general weapon attack does not carry that stipulation with it.
Green-Flame Blade is actually a spell with a range of 5ft that includes a melee weapon attack as part of the spell, and that it must be "A melee attack with a weapon against one creature within the spell's range.."
PHB page 204:
Targeting Yourself: If a spell targets a creature of your choice, you can choose yourself, unless the creature must be hostile or specifically a creature other than you.
So it seems that this cantrip can be targeted on yourself, AND the melee weapon attack that you must make as part of casting it can also target yourself, all under cited RAW.
The only two things you must overcome to successfully do this is first beating your own AC (Armor Class) with an attack roll as per PHB pg 194: 'Resolve the Attack', and second; surviving whatever damage your melee weapon attack roll does to yourself (and the damage of this melee attack get's stronger as your cantrip scales in power with your character level). So it's not an effective way to get an automatic, no-roll hit on an enemy.
Best Answer
Only the first target of Green-Flame Blade takes damage from Absorb Elements
The additional damage from Absorb Elements only applies "the first time you hit with a melee attack". When you cast Green-Flame Blade, you only make a melee attack against one target. The damage to the secondary target does not involve an attack roll. Hence, there is no ambiguity: the target of your melee attack takes the additional damage (if you hit), and the secondary target of Green-Flame Blade does not.
The only situation where the extra damage for Absorb Elements could possibly apply to more than one target would be if a single attack roll applied to multiple targets. And even then, it would be up to the DM's ruling, since the spell's text is unclear in this case. However, I'm fairly certain that no player-accessible features grant such an attack, and I don't know of any monsters that have attacks like this either. If an attack has multiple targets, it will generally either require a separate attack roll for each target, or it will instead require each target to make a saving throw.