According the novel's main character, no, the past cannot be buried. While one can believe that he has buried the past, Amir states in the first chapter that the past has a way of "clawing" its way out again. This statement establishes one of Hosseini's stylistic tendencies--challenging cliches of both Afghan and American culture.
Specifically, in the novel, Amir certainly has not been able to put aside the immense guilt that he feels for betraying his best friend, and years later when he has established a life for himself in America, Rahim Khan calls out of the blue from Pakistan, and Amir's past comes flooding back. Like Amir, Baba tried to bury his past, but even though he is physically dead near the novel's end, Baba's past (fathering Hassan) is resurrected by Rahim Khan and motivates Amir to seek redemption for his own past.