Is it OK to go ahead with the surgery if you get sick the week before, or should you postpone?

Hi and great question.I think you should postpone the surgery; but ultimately that is up to your surgeon and based upon where you are in the healing (post-cold) timeline. Best of luck

Depends what you mean by "sick". A common cold may not be a problem while a pneumonia is a major problem. Check with your surgeon. 

Each case of illness should be evaluated on a case by case basis.  Having a cold lets say one week before surgery is ok if you are better by the surgery date.  Sometimes it has to be postponed.