Start date change after TN approval

Hi Guys, I've been looking for a proper answer to this and only found a couple of old posts that were semi-related. Hoping to get some clarity.

Start date on offer / support letter: March 31st Planning to go for approval on: March 24th

Assuming TN is approved, if start date is pushed to April 7th (1 week later), do I need my employer to update my offer and / or support letters in case the border officer asks for the documents?

Thank you!