On its own, not very well, as there are too many arguments on how to tamper with the contents to make it 100% reliable. All these registrations and other forms of "protection" give you is more evidence should you need it. Although you may be able to deter some with threats of litigation, copyright infringement is worldwide, and if you are dealing with foreign jurisdictions (as I am), the cost of litigating becomes astronomical, and there are many countries that don't recognise copyright in the first place.
As for script shopping, I have no experience in this, but I can only assume the parallels to the music industry will require an agent on your behalf if you are looking to reach the majors. If the script doesn't require a multimillion dollar budget, there are independent filmmaker's groups that might be a possibility. Actor/screenwriter Jon Jacobs has produced/released a number of indie films through Zero Pictures, although I don't know if that group is still going or not. Depending on the material, something like that might be an option.