The implication (from the Buffy Wikia) is that she "resurrected" Warren. We know that the First can imitate those who've died and come back since it imitates Buffy at one point.
The real Warren, however, returned months after the destruction of
Sunnydale. Seconds after he was killed by Willow, Amy used her magic
to resurrect Warren and keep him "alive" despite his lack of skin. He
was the one who gave Amy the idea of cursing Willow in order to become
him, and he bore a considerable grudge against both Willow (for
flaying him) and Buffy (for ruining all of his plans)
In the comic serial (Buffy Season 8 #4), Warren notes that his "human life" ended when Willow attacked him. Since his sole means of survival is Amy's magic, it's probable that he's classed as undead rather than magically alive.