Multisite Wordpress setup (wp-multi-network)

I would like to begin blogging for our customers and manage the plugins and updates on a single server. To achieve this, I plan to set up a multi-network instance using the subfolder approach, rather than using subdomains. My question is, will this approach still have a positive impact on the search engine rankings?

For example, let's consider a customer's site, site1.com, which already carries authority. If we create a new section on this site, site1.com/blogs, and host the blogs on our server, will this new section inherit the same authority and rank effectively in search engine results?

I welcome any advice or insights on this matter. Thank you!