Do I need a blog on my store to use it?

If you want to host partners' guest posts, yes. Approved posts are published on the first blog of your store, and without one the host sees “No Shopify blog found to publish this post.”

Shopify stores usually come with a blog called News. If you deleted it, create a new one under Online Store → Blog posts. Your partners need a blog too, since that is where your guest posts go.