But to answer your question, no you don't need to file it:
You may file Supplement A only if:
1. ONE of the following applies to you:
A. You are or were the principal beneficiary of an immigrant petition or application for permanent labor certification properly filed on or before January 14, 1998, which was approvable when filed; (nope)
B. You are or were the principal beneficiary of an immigrant petition or application for permanent labor certification properly filed on or after January 15, 1998, but on or before April 30, 2001, which was approvable when filed and you were physically present in the United States on December 21, 2000; (nope)
C. You are or were the derivative beneficiary of an immigrant petition or application for permanent labor certification properly filed on or before January 14, 1998, which was approvable when filed; (nope)
D. You are or were the derivative beneficiary of an immigrant petition or application for permanent labor certification properly filed on or after January 15, 1998, but on or before April 30, 2001, which was approvable when filed and the principal beneficiary was physically present in the United States on December 21, 2000; or(nope)
E. You are currently the spouse or child (unmarried and under 21 years of age) eligible to accompany or follow to-join a principal or derivative beneficiary described in Items A. - D. above. (nope)