Is there any place that documents exactly what abilities a role is granted when "Core Administration Permissions" is checked? I've see a list of difference between Core and the default Administrator role, but I haven't found anything that details exactly what a role can do when that box is checked.

There is a table in this SA - did not go through it in depth https://suiteanswers.custhelp.com/app/answers/detail/a_id/82465/loc/en_US

Thanks! That table is a list explaining the difference between "Core Administration Permissions" and the default "Administrator" role. It's essentially a list of what CAP doesn't allow.