Yes, the materia inside her hand was apparently already cracked and -- despite giving her strength on par with Sephiroth -- was draining her life energy as a result. It was also supposed to be able to summon Zirconiade on its own, though, but was unable to because it was damaged:
DarkAngel's translation said:
Shears
The summon that will rend asunder the world in a burst of flame: Zirconiaide. Originally, that materia Elf・s got fused in her arm by itself should have been able to call it into being. It's been damaged, so it can't do that anymore. If it's just left alone, the summon won't initialize and the world will be safe. But because it's damaged, it's compensating by draining her life force. If we just leave things the way they are, it'll keep draining away her life until there's nothing left for her to give. She'll die.
LH Yeung's translation said:
Sears:
Zirconiade, the creature that will burn the world, could originally be summoned using only Elfe's Materia. However, it can't be used to do that now due to its deficiency. If it's left the way it is, the creature won't appear and the world will remain at peace. But Elfe's life is being absorbed because of the Materia's deficiency. All of Elfe's life will eventually be absorbed completely and she will die if we leave it the way it is now.
Now, while cracked, the materia within Elfe was not already shattered. This is a misunderstanding of BC's story I've come across before, in which people have misunderstood the role of the four materia that AVALANCHE and the Turks seek out during BC.
The misunderstanding in question is that those four materia and the one in Elfe's hand were fragments of the Zirconiade materia, previously shattered before even Elfe's implant. The four materia sought out during BC were actually Support Materia that aided not only in summoning Zirconiade despite the main materia being cracked, but also facilitated its restoration to full power if the combined five materia were given directly to the summon itself.
Anyway, as seen in this video, once Zirconiade was summoned, the four Support Materia combined with the main Zirconiade materia to create a single materia:
http://www.youtube.com/watch?v=gGI-I-zJfBY
Soon after, Fuhito placed this combined materia into his body, and transformed as a result. When he and Shears killed one another, the player's Turk then comments that the materia was shattered into pieces.
All this can be seen in this video:
http://www.youtube.com/watch?v=m3eMZtexZHw
Note, by the way, that even if the materia had previously been shattered, that still entails that materia can be broken and their function impeded. It had not been shattered prior, though, and yet its function was still prevented with the materia in Elfe's hand being simply cracked.
As well, Shears speaks of destroying the Zirconiade Support Materia once it had been summoned, in order to weaken the summon and allow it to be defeated:
DarkAngel's translation said:
If Zirconiaide is summoned using the method I just explained, it'll still be incomplete. Without the four support materia in place, the summon can't be sustained. If we destroy them, we'll have a shot at taking down Zirconiaide.
LH Yeung's translation said:
By summoning Zirconiade this way, it will be in an incomplete form. Without all four Support Materias, it won't be able to maintain its existence. So in other words, if we can destroy these four Materias, it's possible that we can defeat Zirconiade.
So BC definitely presents the idea that materia can be destroyed or even just damaged to the point that their function is no longer available.