No. To be a legal document it must simply be signed in the presence of two witnesses. These witnesses can be any two adults who are not beneficiaries within the Will. They can be friends, neighbors or co-workers. They can also be related to each other, but they do not have to be of any particular professional standing.
Notarizing your Will is actually going through the steps of having your witnesses sign an Affidavit of Execution in the presence of a commissioner of oath. They are effectively swearing under oath that the Will was signed correctly. This can be a useful step.
After you have passed away, your Will is presented to the probate courts by your Executor, where it is accepted as your legal Last Will and Testament, and your Executor is granted the authority to act as your estate administrator. However, this is the point at which people can challenge the Will, and one of the grounds for contesting the Will is that you were put under pressure to sign something you didn't want to sign, or that you had lost competence and really had no idea what you were doing. In summary - irregularities in the signing process.
If this happens, then a judge will call upon the witnesses to swear in court, under oath that the signing process was conducted correctly, and there was nothing untoward going on. Having your witnesses sign an affidavit at the time of signing does this proactively, so the witnesses wouldn't be called to testify - they have already sworn under oath that the signing of the Will was conducted appropriately. Having the witnesses sign the Affidavit at the time of the Will being signed is sometimes called "self-proving" the Will. Most US States accept a self-proven Will (although not all). In other words, no State requires that the Will be notarized (an Affidavit be attached to it), but most States allow it.
But what if you don't have your witnesses sign an affidavit and your witnesses cannot be found after you pass away, and then somebody challenges the Will? A judge will make a judgement based on other evidence. It could be from a physician's testimony, handwriting experts, and the contents of the Will itself. For example, if you were 98 years old and updated your Will to give everything to your nurse, thereby disinheriting your entire family, a judge may over-rule some or all of the Will.
In summary, the notarizing of your Will is not a requirement, it does not make your document any more legal. However, it is an option and may be useful particularly if you feel that your Will may be challenged or contested.
If you decide to have your witnesses sign an Affidavit, Notary services are available at any UPS office.