I've been home from cycling nearly two weaks now with a pretty bad multi-cold-infection-thing.
If it's just a running nose: sure ... no problem ... go train.
But if it's an actual illness that makes you feel ill all day long ... nah ... stay home.

There's nothing wrong with taking a week or two to rest and not do any training at all, you know.
Two weeks will not make you less fit and will give your body the time to fully heal possible injuries ... even those which you might not know about yet.
Taking some time off can also empty your mind a bit and give you renewed mental strenght afterwards.