Not normally, due to action economy limitations
First, you cannot cast distorted spells, you can only distort spells, once they have been cast. Here are the countermagic rules on how to distort a spell (p. 466, Exalted 3rd. Edition):
Distortion
Once a spell has been cast, its effects cannot be undone, but a skilled sorcerer may mute, twist, or weaken them with a distort action. (...) spells, such as those that last only for an instant or that summon a being that exists independently of the spell, cannot be distorted. (...) As with countermagic, the sorcerer needs to be within short range of the spell’s target or effect, and must be initiated into that spell’s circle. (...) Distortion is a combat action that cannot be placed in a flurry.
Distortion itself has no limits on another's spell like Countermagic1, or on an enemy's spell. It simply refers to a spell that has been cast and a sorcerer skilled in the spells circle and in range.
However, unless you have some way to get more than one normal action, you cannot cast or sustain and distort the spell in the same turn, because that would cost you two actions. The general rules for actions are (p. 195):
Characters can normally take only a single combat action per turn, and receive only one turn per round. There’s an exception to this rule. Characters are allowed to declare that they’re taking a flurry.
Casting the spell is a combat action and can't be used in a flurry (p. 465): The shape sorcery action itself is a combat action which cannot be included in a flurry.
Distortion is a combat action and can't be used in a flurry (p. 466): Distortion is a combat action that cannot be placed in a flurry. Sustaining the cantata also costs you a shape sorcery combat action:
Once the sorcerer has begun the Cantata of Empty Voices, she may sustain it with an unrolled shape sorcery action taken on each subsequent turn at no additional cost.
As neither of these actions can be put in a flurry, and you can only use one non-flurry action per turn, you cannot cast and distort, or sustain and distort your cantata.
P.S. If you had a way to get two actions in a round, I think it could work.
1 While Distortion is a subheading under Countermagic, and the paragraph for Countermagic starts with One sorcerer can unravel another’s spell as it’s being shaped. (emphasis mine), my reading is that limitation does only apply to actual Countermagic, as you cannot even distort a spell while it is being shaped, only once it has been cast. The sentence that "As with countermagic, the sorcerer needs to..." in the Distortion rule also supports that Countermagic is similar, but separate from Distortion.