The short answer is: Yes.
A Living Will is a document that only becomes relevant once a person is determined to be terminally ill by two physicians. It allows you to make the choice regarding whether you want artificial life sustaining procedures to be used. You are also able to decide whether or not you want nutrition or hydration to be administered. This document can be used as a back up. Should the person you have appointed as your Power of Attorney for Healthcare be capable of making decisions for you that is the first choice. The Living Will is there to provide that your wishes are known.
The Durable Power of Attorney for Healthcare covers the types of situations in which your Living Will may apply, but is not limited to such circumstances. An example, is if Thelma was in surgery and due to some unforeseen complication the doctor needed to pick between whether she would lose her hearing or her eyesight. The Durable Power of Attorney for Healthcare would presumably be someone Thelma was close with and trusted to make such decisions for her; her sister Louise. Louise knew that Thelma’s deepest passion in life was her amateur photography. Louise could state that Thelma would want to keep her eyesight, rather than a doctor who did not know of Thelma’s love of photography.
It is important to plan for all contingencies. What if in the above example, Louise had recently driven off a cliff and Thelma was on life support? Rather than a long and drawn out legal battle, a Living Will would indicate to the doctors what Thelma wished. It is a gift to your loved ones to make such wishes known before they become an issue.