The short answer is yes. A Will and a Power of Attorney are two very different documents used for two different purposes. They both may require the people you have appointed to do certain acts for you under your Power of Attorney and your Will to make certain decisions on your behalf but one of these documents finishes and cannot be used when the other one becomes valid and comes into use.
A Power of Attorney is a legal document in which you hand over your authority to someone else to manage your finances and make decisions for you in the event that you cannot or are unwilling to do so yourself. A Power of Attorney is only valid during your life and any authority you have given to others under this Power of Attorney, immediately ceases upon your death. The Power of Attorney is then no longer valid. All acts done under the Power of Attorney are still and will remain valid but any acts done under the Power of Attorney after your death will not be valid.
Once you have passed away this is when your Will becomes the primary document appointing someone and giving them authority over decisions regarding your estate, finances and affairs. The Executors listed in your Will may have a role similar to the person named in a Power of Attorney does before your death depending on the power you have provided to them, but the power your attorney had under your Power of Attorney becomes voided and can no longer be used to manage your affairs after your death.
In addition to your Will …
In addition to your Will and should you require further decisions by someone you may appoint, you can also make a Living Will, also called an Advanced Care Directive or Anticipatory Direction in New South Wales. There are equivalent forms and procedures in most Australian States that enable you to make the same appointment. The Living Will stipulates your medical wishes should you become unable to do so and is often created by people who have a terminal illness. If you do write a Living Will you should also create a Power of Attorney as their functions vary.
A Living Will could be created for specific things regarding your health towards the end of your life and a Power of Attorney for other decisions outside what is in the Living Will such as financial matters. It is important to note that the law regarding Living Wills varies in different states in Australia so legal advice should be taken so you completely understand the outcome should you decide to write a Living Will.
If you have a Power of Attorney, the person you have appointed will not have any control over your affairs after your death and if you die without a Will the courts will take control and decide how your assets will be divided. If you die without a Will, whether you had a Power of Attorney during your life will not make any difference at all to the distribution of your estate and assets in the event you die without a valid Will.