Change domain instance target within Multisite

I’ve not worked with Multisite before. So I have what I think is a quick question, yet I have not found a direct answer.

In the site I’ve inherited, there is a live site and a staged, new version of that site. The staged version load via domain.com/staging-site and obviously the live site loads through domain.com.

Can I simply change the Site Address and Siteurl and Home paths via the Domain Mapping at the Network level? I believe Domain Mapping is a plugin that was added.

It seems like I could just change the site instance which is set to load by the main domain and that would be it. However, I don’t know if that is true or if database updates are required etc.

I’m not moving anything. Both sites already exist within the multisite setup. I just want to change the instance that is live on the main domain. Is it that simple?