Good question for thought. If you are using the lab for finished product, water, environmental testing, etc. as COA to an end user then I would suggest your practices be accredited to ISO 17025.
If you are using an external lab for COA, then no I can't find any reason why it would be necessary.
I think the following is of interest from the ISO 17025 Handbook.
"It is not uncommon, however, for organisations with laboratories used purely for internal
quality control purposes to seek to accredit the laboratory to ISO 17025. This is generally
done to enhance the laboratory’s, and hence the overall quality control system’s,
credibility or as part of the application of an ISO 9001-compliant system."
Sub ISO 9001 for whatever GFSI system you are working towards.