What are the potential consequences of removing local admin access via group policy (2003 domain)?

Currently, all users on our domain have local admin rights.  This is not a group policy; accounts are just added to the local admin group during individual setup.  We would like to remove these previously added admin privileges, but I wanted to check with you guys before I just stepped through a tutorial and enforced the policy.  What are some potential issues that I may be facing?  I do have an alternative method for distributing software updates, but I was wondering if this local admin restriction would effect domain admin accounts as well. If I log onto a PC with a domain account, will the policy remove that account from the local admin group or will the domain admin status supersede the policy?  Thanks for reading.