I worked overnights for 25 years (11pm to 7 am) and got sick with the flu at work 3 or 4 times in all those years. Often i was the only one on duty so there was no way I could go home. I would tell them I was taking the NEXT day off sick, and usually I was well enough the next day that I COULD have worked.
I have an unusually knack for getting sick of getting sick on Friday after work, and being better by Sunday night, so being sick work hasn't been much of an issue.