Starting at Level 3, any Artificer that is not a Warforged (or presumably Bladeforged, seeing as how that's a modified Warforged Iconic) can take Construct Essence. Later, starting at Level 12, they can take Improved Construct Essence to turn themselves into a living construct, like the Warforged.
As far as I know, Living Construct is a type, not a race. The DDO Wiki (which I understand is not always accurate) says that taking that makes the PC a living construct instead of their original race.
Is their race listed as "Warforged" or "Living Construct" in place of what they started that life as?
Also, I presume that your appearance does not change with Improved Construct Essence because it does not for the previous level of Construct Essence. Is that accurate? I'm asking because my highest level character is not a high enough level to take that feat.