Exchange 2013 - Full access to mailbox but don't add to Outlook 2013 profile

Use the following command in Exchange Powershell (admin mode).

Add-MailboxPermission -Identity KrazyK -User KrazyAdmin -AccessRights FullAccess -AutoMapping:$false

Run above command script to give domain access to mailbox, change KrazyK to logon username. The AutoMapping false command will ensure it does not copy mailbox to KrazyAdmin Outlook client.