The simple answer is yes. A pizza restaurant does need local or national SEO depending on the size of the business.
There are only a few major pizza chains that stand out; such as Domino's and Pizza Hut, while the vast majority are fighting for a small piece of the pizza market that is left over by these national chains. Therefore, having a pizza restaurant can be a very profitable business, if it can capitalize on the online traffic in your area and get some of those customers looking to try something new. This type of local business is profitable in almost any market and can be easy to maintain. By using the power of the Internet and doing a proper, effective SEO program for your pizza business, you can tap into you a the local audience. Most of the highly successful pizza restaurants have a strong SEO marketing program that targets online orders, increases delivery orders and ensures that their customer base can easily find their business.
When customers have an awesome experience both in your restaurant and on your digital restaurant, this increases your restaurants's image, your brand reputation. Many of your customers have their own network of friends on various social networking sites and platforms. Now imagine a site that only list the reviews you want and offers them via SEO to the public.
Search engine optimization works, even in small restaurants. It is all a matter of understanding what it takes to rank highly on Google and Bing as well as other search engines in the world.