I don't believe so. It seems like there may be three different Zadoks in The Bible. There are some listings for sons of Zadok, but Buzi isn't among them.
I only see one listing for Buzi, in Ezekiel 1:3. It doesn't list his father.
ezekiel
2 Samuel 8:17New King James Version (NKJV) 17 Zadok the son of Ahitub and Ahimelech the son of Abiathar were the priests; Seraiah[a]was the scribe;Interestingly, at the Coronation of King/Queen of the United Kingdom, there is a song mentioning Zadok, quite prominently.
Zadok Domnitz was born in 1933.
Zadok Magruder died in 1811.
Zadok HaKohen died in 1900.
Zadok HaKohen was born in 1823.
Zadok Casey was born in 1796.
Zadok Casey died in 1862.
Rachel Zadok was born in 1972.
Heidi Zadok is 5' 1".
Zadok Magruder was born in 1729.
The cast of Buzi - 1997 includes: Giga Bokeria Gela Gabedava Tea Kantidze Giorgi Khubua