Yes that should work fine.
1. Use the same connection string in all sites.
2. in the first site set the Web.config "AllowMultipleSites" = true
3. Now both sites are the same content, to make the new site have its own content go to the first site in Admin > Site Settings. You'll see a dropown next to the site name, choose "New Site", give the new site a name and click save.
4. Now more controls show up at the bottom of the page to configure the host name for the new site and which features to include. Add a host name that points to the second site and now it is independent, it no longer shares data with the first site.
I just updated the documentation for this here:
Please let me know if the documentation is unclear or any feedback to improve it.