We are taking a system that was in equilibrium and we introduce a huge disturbance (+ multiple degrees C). Hell yes it will be unstable until it reaches the new equilibrium (whatever that equilibrium will look like - catastrophic for life or not).
From what I know about climate on Earth, it has literally never been in equilibrium — see periodic ice ages with glaciers up to 3—4 km thick, or periods of warmer climates when plants grew in huge amounts at latitudes where we have now vast oil reserves in Siberia.
