To the best of my knowledge, none of the GCP/TMF regulations provide an answer to this. Some regulations require documents to be signed using an advanced electronic signature and DocuSign signatures are usually regarded as such.
In my opinion, the issue here is one of trustworthiness. In legal terms, the document is legally acceptable without the Certificate of Completion. And from a regulatory perspective, it meets the requirements without the Certificate; it shows who signed the document, when, requires security to apply the signature, and is linked to the document so that any change is detectable.
The Certificate of Completion simply provides additional evidential weight to the signature, providing additional metadata concerning the signing sequence of events. This information is rarely provided or available for traditional wet-ink signatures (other than those witnessed by a notary, for example) so it does not seem reasonable to expect electronic signatures to have a “higher burden of proof of authenticity”, especially considering digital signatures are typically more robust, secure and trustworthy than wet-ink.
I see some sponsors retain the certificate with the signed document but most are not retaining the certificate.