Можно ли реализовать интерфейс на классе Linq2Sql?

LinqToSQL classes are partial classes, so you can have an additional file that implements the interface for the LinqToSQL class.

Just add this to a new file, using the same class name as your LinqToSQL class:

public partial class LinqToSqlClass : IFoo {
    public void Foo() {
        // implementation
    }
}

If your LinqToSQL class already implements the necessary proporties you should be able to only include the interface declaration.

To answer the comment about using a differently-named LinqToSQL property to implement the interface, you can use the syntax above and just call the LinqToSQL property from the interface property, or to keep things a bit cleaner, use explicit implementation:

public partial class LinqToSqlClass : IFoo {
    void IFoo.Foo() {
        return this.LinqFoo(); // assumes LinqFoo is in the linq to sql mapping
    }
}

By using this syntax, clients accessing your class will not see a redundant property used only for implementing an interface (it will be invisible unless the object is cast to that interface)