What happens to a local user on a Windows 7 computer after being added to a domain?

Question

Domain name market

There is a Windows Server 2008 R2 CD. I used to connect only clean computers to the domain. Today the task came to add the user's personal laptop to the domain, he will come to work with it and connect to the local network.
And here are a few questions: what will happen to the user he used? When he is at work, will he write domain\user to the login, and when he returns home, will he write computer_name\local user? Our domain uses a proxy server configured by group policy, what will happen to it when, for example, it uses the Internet at home? Is there a GPO with a local administrator, in the OU in which the computer will be located, do not add this GPO?
What other pitfalls can occur when adding a working, private computer to a domain?

Answer 1

as it was and will be
the GPO for local users will not work
, you need to log in like this .\login

Answer 2

Oh , nonsense. If you enter a camp into a domain, then all container policies will apply to it. And it will affect the local user too.