I would answer No because of atmoshperic escape.
If a world is broken into several pieces the main problem would be that the gravitational pull of those pieces will probably not be enough to maintain an atmosphere around it.
Without this gravitational force, the atmosphere would disperse into space within a few seconds and it would lead to death all life on any biomes.
Source here :
Gravity is what keeps a planet's gaseous atmosphere from spreading out into space away from the planet. If we compare the gravitational pull of each planet in our solar system we would find them to be different. This is because a planet's gravity is related to its mass.
Here you have all details about atmospheric escape parameters.
Moreover, because life is adapted to it's environment, if a world would shatter into several pieces, even if those pieces are big enough for to maintain an atmosphere of their own, life would not be adapted to this gravitational change. Why, because their mass is adapted to the original gravitational pull.
Let's say that earth is broken into small pieces. One is the size of the moon and let's assume that it can maintain an atmosphere for us to live. On the moon, gravity is far lower than on earth. Astronauts need very heavy boots to walk on the moon. As we are, we could not live on the moon even with atmosphere.
From a weather point of view, there would be a huge modification of atmospheric pressure. Life could survive but the biome will not be the same as before the blast.