The issue of the PC's potential tempering actually is addressed in a fireside chat with Ardbert('s spirit) during the Shadowbringers MSQ; he says it doesn't much matter since we'd be doing more or less the same things anyway.

Hydaelyn's blessing could be considered tempering, but if it is it's more of a placebo type of deal that doesn't appear to do much of anything other than prevent other primals from claiming our soul. Even that much is in question, given it's the Echo that prevents our tempering, not Hydaelyn's blessing - and we had the Echo before even a fraction of the blessing, so logically speaking we can't be tempered. (Except maybe by massive effort from an unfathomably powerful primal. Even Shinryu couldn't do it.)

The PC doesn't do good because they are compelled by Hydaelyn, the do so because it's who they are down to their very soul.

If we were tempered, an Angelo treatment would cure it; but nobody ever sees any sort of corruption, not even Y'shtola with her aethersense (after the Lightwardens' corruption is cleansed following the showdown with Hades). Besides which, if we were tempered, would we be able (or have to) question whether or not that's the case?