I'll cut to the chase; In my view, yes, you do. But maybe not for the reason you think!
I'm surprised how few of my clients have a LinkedIn profile. The reasons are myriad, but there are themes that repeat. Folks who aren't fans of social media have concerns about their information being "out there". Details about work seem particularly private. Having not dabbled in LinkedIn before, people feel concerned to dip their toe in the water for fear of unknowingly committing some career limiting move.
When I first began my work as a career development practitioner, one of my managers advised me to "be sure and tell your clients to fill their resumes with key words, so that the search engines can find them." I'm happy to say I didn't take that advice then and I don't promote it now. I think a person is likely to hire you for your next job, not a machine. To that end, the thing I value about LinkedIn is not all the fancy algorithms and tricks; it's how it allows you to connect with people.
In my opinion, one of the most helpful things about LinkedIn is your photo. People are hard-wired from birth to respond to human faces. Showing a picture of yourself immediately "fleshes out" your resume from the two dimensional page to an actual person. Even if your written profile is bare bones, adding a photo to your profile makes a great bridge from the paper version of you to the real you.
Let's face it, when you're applying for jobs, people are going to "google" you. They may find your social media presence on other sites, stumble across times you've been mentioned in the news, see your white pages listing and so on. When you are job hunting, you can think of your LinkedIn profile as your marketing brochure. A picture is worth a thousand words, so introduce yourself to prospective employers by showing them who you are. You can choose how to present yourself here, so choose wisely.
A great website I love is http://www.photofeeler.com. It's full of great tips for easily crafting a terrific photo for various social media audiences. You can upload photos and get other users to rate how they perceive you based on the picture. It's a fascinating exercise to upload several snaps and see how the results compare.
I know some of you may be cursing me through your computer screens, with valid arguments that how one looks has no bearing on one's ability to do a job and should never be a factor in the selection process. Of course, that is true. It's also true that showing prospective employers that you are a real person, especially if you are perceived as friendly and professional, may well put your resume into the shortlist pile for interview.
I don't recommend mass distribution of your resume into the black hole of the internet in the vain hope that some machine somewhere will decide that the collection of words you've strung together in your resume has deemed you their perfect match. I do recommend corresponding with real people, having genuine conversations about their business needs, and telling them about how you might add value.
Your picture adds a human touch that reaches across the ether to help you connect with other real people via LinkedIn. Isn't it worth a try?