Life wouldn't develop there, but if life used to cover the surface of Mars, and largely died over time, but was still surviving in some places, this would be one of the likely spots.
The biggest problem would be if the changes Mars underwent were too fundamentally anti-life for anything to survive whether it was in a cave or anywhere else.
In my opinion, we're going to find out on Mars that there are forms of microbes that can hang on in sedentary 'ready' state for a billion years, in extreme environments, just waiting to jump back to activity. Most of Mars will be barren, but there will be small pockets of microbes (most likely in a sheltered cave, under ice, or similar) in a form of extreme suspended animation.