Battling cancer is a consuming process, and I think that it is important to take off as much time as necessary to concentrate on getting better. My bank account would probably take a hit, but that's better than my health declining more rapidly because I chose not to slow down.
Is this a serious question? What is up for debate here? Of course I would take time off of work to complete treatment to get rid of CANCER! If my work didn't allow it then they would be down one more employee. My health is a big priority in my life and should be seen that way in others eyes too.
Cancer is one of those illnesses that can kill you if you don't seek treatment and work on getting better. In Mortensen's situation, there is already a culture there at ESPN where they had one anchor--Stuart Scott--work through his cancer, and it gained a great deal of publicity. He's dead now, and while he was alive, Scott admitted that he had begun the heavy workout-work through regimen he was on after the cancer had gone terminal. Don't let it get that far; take the time to get well, whether that means surgery, chemo, or both.
If I was battling cancer of any kind, throat or otherwise, I would most certainly take time off work to be treated. You need to rest in order to heal properly, and the stress of work would delay recovery as well. It doesn't make much sense to work when treating cancer.