With Drupal (and many other CMSs) you don't need to have a separate domain for the admin area. Users simply login at domain.com/user/login.
If you especially want to use admin.domain.com as the login URL for users then a redirect would do fine, it is a kindof cool address.
But if you are thinking of writing your own code to get the content from the Drupal database for your main site then you are (just slightly) under-using Drupal. It is both the Content Management and Content Display platform and you would be creating your own version of the theme layer and hooks etc (might be fun though - definitely faster :).
The only advantages I could see in spreading out the admin (logged in) area of Drupal across to another domain would be in using a website caching service or some custom security for some reason.
So my advice is:
Yes, you can install Drupal on a sub domain, it is a domain in itself.
But no, don't bother having an admin domain and writing your own code to get the content from the database. Use Drupal for what its good at.