There is no good reason to do this. The
SomeDomain\SomeUser would not be authenticated on that local machine. Even if SomeUser was an administrator/domain admin on SomeDomain, it would still not do any good on the local machine. If it would, that would be huge security holes with Windows and allow me to bring a laptop with my own domain controller on it and then access someone's computer on that same network (ie, coffee house).
In order for SomeUser to do anything on that local machine, you would have to have local admin rights to that machine to join it to the domain. From there you would be able to use SomeUser to perform whatever necessary actions.
Ah. That is not really the same. When you open up the SQL Management Studio, it will ask you what server you want to connect to. This is basically asking you for authentication of a user who has access to that SQL Server. In this scenario, different from your original question, would be able to select the Server that you wish to connect to, valid user who has access to the SQL Server and password. You're accessing a network resource that is part of the domain and will need to authenticate with a user who has access to the resource on that domain. In your scenario, this will work.