You will always get "SomethingElse". This is because ConstantB depends upon ConstantA.
You can even switch lines and you'll get the same result. The compiler knows that ConstantB depends upon ConstantA and will handle it accordingly, even if you write it in partial classes.
To be completely sure you can run VS Command Prompt and call ILDASM. There you can see the actual compiled code.
Additionally, if you try to do the following you'll get a compile error:
private const string ConstantB = ConstantA + "Else";
private const string ConstantA = "Something" + ConstantB;
Error: The evaluation of the constant value for 'ConsoleApplication2.Program.ConstantB' involves a circular definition
This sort of proves the compiler knows its dependencies.
Added: Spec reference pointed out by Jon Skeet:
This is explicitly mentioned in section 10.4 of the C# 3 spec:
Constants are permitted to depend on other constants within the same program as long as the dependencies are not of a circular nature. The compiler automatically arranges to evaluate the constant declarations in the appropriate order.