Answer:
You can say that Mercutio did believe in destiny and he even saw things in the form of an omen.
For example, when Mercutio says: "a plague on both your houses" after the bloody struggle that resulted in his death, he wants fate to punish the Capulets and the Montagues for what they have done to him.
And indeed, a "curse" falls on both families, which ends with the death of Romeo and Juliet.