Although I know a bit about networking, I don't pretend to know about domains. However, as you've had no other replies, it is my understanding that if the computer is set up to operate in a domain, it has to be removed from the domain before it can be used in any other network situation. This will probably include connecting to a router for internet access.
I have heard of situations where people have tried to start the computer when not connected to the domain and when the login fails, they are locked out of the PC. I suspect that having separate User accounts won't be sufficient to get round the issues of using the computer outwith the domain.
If you have IT people at work, seek their advice because it isn't a straightforward issue.