Short answer? Yes, yes you do. Here's why.
A lot of startup founders tend to under value designers and the many ways they can help their business. This is usually because designers are only seen as people who draw pretty pictures. Don't be fooled! Designers are not artists, they are highly efficient problem solvers. If you hire the right designer, there's almost nothing they can't help you do.
For example: Are your users misusing your app? Are they confused by the functionality you offer on your website? Having trouble refining your pitch? Not sure what revenue model to go with? A designer can be extremely useful in helping solve all these problems.
You'll still get the plethora of visual-based tasks they can do when the time is right—pitch decks, web design (even development), layouts, ads, photography, app UI, business cards, etc.—but there are many things you can get them to do before you'll need any of these. Designers are seen as a luxury only bigger business can afford. If you manage your designer correctly, they're worth more than their weight in gold during the early stages of your start up.
Of course, like any other employee, it's very important not to overload them. Once you see their potential, it's very easy to go overboard and waste your designer's time; getting them to do pointless tasks and design things that aren't necessary. Too often I've seen designers, 2 weeks after they're hired, spending days on a task that will probably never be seen or used by anyone. That's when you start to waste money, which is where all these misconceptions stem from.
So if you're looking for a super ninja to help you understand your business, help communicate with your users and help solve some of the fundamental problems your business may run into, think twice about hiring a sales person, a business strategist and a marketing manager. Get the whole package plus more and hire a designer.