Don't see why not. I would even rule that death ward stabilizes the character in this scenario.Had an interesting question come up in game tonight, and I'm curious how you guys would have ruled.
Does death ward protect against dying from a third failed death save? Does that final failed save count as "an effect that would kill it instantaneously without dealing damage" for the spell's purposes?
Death ward normally triggers when you drop to 0 hit points, so if you're under it while making death saves, it means somebody cast it on you after you were already reduced to 0. If you want to burn a 4th-level spell slot to cast spare the dying, go for it.