I’m probably misunderstanding this. >
First ICH E6 (R2) is a really good guideline on GCP and should be consulted every time.
The persons delegated to take consent and inform subjects should be suitably qualified by education, training and experience. They should be formally delegated that duty by the Principle Investigator and that should be signed off (& contemporaneously dated) on the Delegation Log before any duties are performed. The delegate should also have documented training on GCP; the details of the trial concerned; and training in how to gain genuine written informed consent.

The person gaining consent should be identified and should sign the consent form at the same time as the trial participant. It would be nest if the person performing the trial related duties was also the person into enter data into the clinic records. If not then it would be best to identify both the person gaining consent and the person entering records. It is also a requirement of good documentation practice (ALCOACCEA) that records and updated contemporaneously. So that would mean entering information very close to the time when the duty was performed. Nothing wrong with documenting all staged of the informing and consenting participants as each stage is conducted.

Your protocol and the submission into Ethics/Regulatory authority will contain details of how subjects are consented. For instance the new EU Clinical Trial Regulation requires two interviews, one for informing and one for consenting. Therefore both will need documenting. Subjects are always given ample time to consider the information presented and this can be as long as the participant wants. Your protocol might stipulate a minimum period.