When you follow a quality standard and it says "shall have", that is generally makes the requirement mandatory.
[p.s. As a courtesy to and good practice for other readers, FAI means First Article Inspection.]
You say you currently have a documented procedure, so yes, you should be able to add details to be in alignment with AS9102C. I recently did the same. I noticed rev C added language (4.6.b) which makes a stronger call than rev B to form a multi-disciplinary team to make decisions. In that way, your changes evaluation is not limited to any one person's judgement. Also, a group might develop a test plan which is more expedient or economical than one person's idea.
On the question
@mig29 asked, I notice the long-used, customary definition of a significant change (potentially affecting fit, form or function) was removed from Rev B to write Rev C. The new standard for repeated FAI is "changes that invalidate or are not represented in the original results". I am not going to interpret the word "invalidate" for someone else, that is why you gather a multi-disciplinary team.
I also noticed Rev C added wording to emphasize that FAI is not a one-time activity, or re-done only after equipment moves or a complete product/process redesign. Instead, FAI could be viewed as a
confirmation step of your organization's existing Change Management procedure. If you haven't seen them, you should read
guidance documents released within IAQG and SCMH 3.2 the same time as AS9102C, which list FAI common mistakes and best practices.
I always consider FAI to be an important risk reduction measure. The FAI with a sample size of one is NOT redundant to more extensive design, production roll-out, and validation efforts, because FAI provides assurance on a different level. FAI might be your final opportunity to catch those annoying errors that sometimes slip through the cracks in your other quality verification efforts.
In this way, FAI is similar to the dock audits I remember doing, thoroughly inspecting one sample of finished product before a large customer order goes out the door. I almost always found one or more details not right. That is how goofs are uncovered, like the labels threaded in the machine upside down because the wording in the work instruction was not clear, or 3 screws were kitted in the BOM when there were clearly supposed to be 4 but the person who designed the kit was different from the person who designed the assembly, or the mill operator read the hand-written 7 and thought it was a 1. I don't think anyone's "risk assessment" is likely to foresee those errors. As long as your FAI uncovers details which are not right, there is value in doing FAI.