You shouldn't do those things just because you can. For 1. You can over extert yourself and make yourself even sicker, and for 2. You will likely spread sickness unless you're in full containment or taking an antibacterial bath every 20 minutes.
I've never been sick enough to be debilitated from being a normal human, but I stay home regardless to prevent the spread.
The only time I stayed home and didn't do my own thing was similar in a way.
Was ~12-13, and woke up at about 4am with one of the most painful migraines ever, probably not a cluster, but the worst pain I've ever felt. Anything and everything aggrivated it. The slightest sound was like ear rape, all light was absolutely blinding, couldn't move anything, and even autonomic things like my heart beat and breathing shot pain into my head. Spent about 8 hours waking up in excruciating pain, only to finally fall back into blissful painless sleep for about 20 minutes to an hour. I've had many more migraines since then, but never to that degree and I typically just treat them like normal headaches. But just because you're not sick enough to minimalistic tasks like play games/watch tv doesn't mean you are capable of going to school or work, because many factors can make your condition deteriorate very quickly.