The emergency travel document is for just that - travel. You have had 49.5 weeks to plan for this, and you may find that your options are very limited. When does his passport expire?
OK, so he would like a 30 day extension, yet he will have overstayed. If you are lucky he will pay the fine and get the extension, however, they could just tell him to leave the country. he could have applied for the extension up to 30 days before (depending on office), so he did have plenty of time to do it.
20 days before is a prime time to renew, the 3 weeks you are thinking about is the under consideration period, don't worry about that, you will still have a valid extension.