Absolutely! The author doesn't mention what type of communication he means, but for business communications (in Belgium, where the author is from), anything over 24 hours (one working day) must have some explanation.
It's always better to explain yourself, otherwise, it looks unprofessional if you reply after a week as though it's normal.
Overall, the recommendations about email look very personal to the author and perhaps shouldn't be taken as general advice.
That’s what out-of-office automatic replies are for, which will include information on what business day you will be back, and often will also specify who is your substitute while you’re away.
"Out of office" just means that you don't access your work email. If that's the case for 350 days a year for you, then the discussion is pretty moot anyway.
It's always better to explain yourself, otherwise, it looks unprofessional if you reply after a week as though it's normal.
Overall, the recommendations about email look very personal to the author and perhaps shouldn't be taken as general advice.