SEO can definitely help you achieve top positions for all of your branded keywords. In most cases, when that happens, you start saving a lot of money by stopping all branded keyword PPC campaigns. However, if you are in a very competitive industry, the chances are that your competitors bid on your branded keywords. In this case, up to 4 adverts of your competitors might appear above your hardly earned organic positions. To make things worse, if the adverts of your competitors promote better offers and services than your business does, then you will lose a lot of potential traffic, and hence, conversions.
Branded searches happen when users are at the last stage of their customer journey, meaning they had visited your website before, shortlisted you and now want to buy from you. Running branded keyword PPC campaigns and using some techniques to take down competitor ads will help you eventually convert those prospects to customers.