While this certainly gets into semantics, I don't think you need a "blog" but a website can help a lot.

I wrote about why most smaller companies don't need a blog here: https://kolemcrae.com/notebook/humblesuggestion.html

You may say: isn't that a blog post? I would disagree. You can read how my website isn't really a blot here: https://kolemcrae.com/notebook/notablog.html

I'd say a website is fantastic for your brand, and combining that with a fantastic LinkedIn profile can take you far. Needing to blog constantly on the other hand isn't as important.