Couldn't the emergency flight have run into some problems, making it take longer and that led to the crew being out of duty hours? Like the flight was supposed

Couldn't the emergency flight have run into some problems, making it take longer and that led to the crew being out of duty hours? Like the flight was supposed to take 3-4 hours but wind and some airport issue caused it to take 5? Something that may not have been obvious until very late in the flight too.