Not all Ilyrians have the same augmentations, is the impression I get. So no, it's not a given, but unless Spock knows specifically what kinds of augmentations Una has - and I don't see that being a given either - the logical (pardon the expression) person all eyes turn to in the face of a high-gravity problem would be him. Even if it's a, "Commander, let me - I was raised on a high-gravity planet," remark met by a "No, I'm XO and I'm Illyrian," retort, that would have been settled.
And as someone on reddit pointed out, even if Spock hadn't been the one to go in, he could have melded with anyone who had been injured in the pod. Nothing in the story need have changed at all except the person involved.