No, the point of the Living Machine option is to have a constitution score so that you can get bonus hitpoints and fortitude saves from a positive constitution score like normal spellcasters. Also so you can get healed and resurrected by spells as normal, and drop unconscious at 0 hitpoints instead of instantly being destroyed, and if you want to use any feats with constitution prerequisites. Oddly enough the Living Machine option does not appear to remove the +10 hitpoints you get as a construct, so Living Machine Wyrwoods make for some rather tough Wizards.