Anyone who happened to read this post of mine yesterday will already know that I think the answer to this question is no. But Julian Borger appears to think the war played its part:
The ghosts of the 2003 Iraq invasion and the furious debates that preceded it still hang in the air. Even though it was not fought on humanitarian grounds but rather on spurious claims of Iraqi weapons of mass destruction, the fiasco and subsequent US and British attempts to justify it helped reverse what was arguably one of the great moral advances of the post-cold-war era: the UN-backed principle that the international community had the "responsibility to protect" civilian populations when their own states were unable or unwilling to.
There's something wrong with Borger's chronology. R2P was accepted by the UN General Assembly in September 2005, some two and a half years after the beginning of the war in Iraq. It was plainly at work in the thinking behind the intervention in Libya in 2011, authorized in UN Security Council Resolution 1973 (which Borger also mentions).
His column is worth reading anyway for its account of how things stand at the UN right now.