For me the question isn't so much if to ride but how hard and how long. It seems like your primary concern is the commute to work. I would probably take the sick day, and go for a ton of rest. But I also get that other kind of sickness - cabin fever. So I'd probably end up going for a nice long, mellow, low effort ride and still get many more hours of sleep than I usually get.

But for me, cycling is more about healing than anything else. I get chronic stress-related headaches and I'm a downright moody son-of-a-*****. Regular, consistent mileage on the bike has done better for those two "ailments" then anything else I know.