I'm not sure I follow what you're saying here.
The local group I've created on my vCenter server is not inside the local administrators group on vCenter.
I have created a new group called 'ESX Admins' which contains a domain group also called ESX admins. My approach is to add domain users into their domain group and by doing so, provide them with full administrative access to vCenter.
However, when I also add the local administrator account from the vCenter server into the local group called 'ESX Admins' I am unable to access vCenter.
I know I've removed the administrators group from having vCenter permissions, but I've not set any permission to say no access, I've simply removed it as per VMware practices.