Yes, it is very important that your case officer be informed. Otherwise, they might think you are ignoring the deadline. As a precaution, you might want to get a copy of the email your migration agent sent to your case officer to make sure they actually informed them?

I've just read posts on this forum about how some people have had issues with their migration agents or they don't get updates,etc.

But if your agent is very good in notifying you about issues and following your direction, then you should be okay.