In a situation where an evaluation is ordered to update values on a special asset credit, not necessarily for renewal or refinance, would we need to send out a notice of right to receive copy of appraisal?

No application for credit - no notice:

1002.14—Rules on providing appraisals and other valuations.

(a) Providing appraisals and other valuations. (1) In general. A creditor shall provide an applicant a copy of all appraisals and other written valuations developed in connection with an application for credit that is to be secured by a first lien on a dwelling.