I only occasionally drink coffee (or tea) and have found that 1-2 days of consecutive consumption are fine, but any more will trigger the withdrawal you mentioned. YMMV probably.
When I started drinking coffee, I drank it only at work. I started to have regular headaches on Sunday. It took me a while to connect the dots and understand I was regularly triggering two day withdrawal.
It WILL vary a lot. I do two weeks of "zero coffee" every year and never had any withdrawal symptoms, the rest of the year I drink a lot of coffee (4 big cups a day). Only sometimes I drink it to be more alert, typically I need it only to code. No coffee - no programming or any creative work for me. I try to mantain constant amount of caffeine in organism by sipping those 4 cups for whole day.
It could be a withdrawal symptom if their ability to work returns after the withdrawal period ends.
I've known people who are completely unproductive if they're not on Adderall, or on cannabis, I can't think of any reason there aren't people who are entirely useless without caffeine.