*** Improved by Wrobinson on 03/16/2008 ***
This question is relatively unclear but I think I understand that it is that you are asking. The answer depends on exactly what you grante administrative rights to — a local workstation or server, or add a user to to a special group such as domain admins, domain administrators, etc. Making a domain user a member of the local administrators group on a particular computer or set of computers does not translate into having domain privileges.
*** End Update ***
If a local user is granted administrative rights to that server they can do anything they wish to that server only. The rights do not traverse back up to the domain, nor do they transfer to other servers in the domain.