Not all policies cover sickness, sometimes it is only redundancy so you need to check the terms to see if you are covered. There's normally a waiting period at the start where you have to cover the first (say) 30 days and only then does the insurance kick in - often it won't make the first payment until you've been off for ANOTHER month after that.

And as stated above, it is usually only going to pay for a limited amount of time.