Copyright exists on any piece of writing once it has been published. In legal terms once the script exists, you have copyright. However, the legal issues over copyright are not over whether you have copyright but in establishing in court the date that the document existed.
The postage technique provides a degree of proof, but as Zen stated it does not provide absolute evidence. Therefore, no lawyer is going to want to go to court with that as the only proof, as copyright cases are almost impossible to win anyway.
The higher your level of evidence the more protected you are from theft, because if the reader knows you have properly established time of publication, then they are less likely to steal your film.
There are two main ways to establish date of publication.
1) Library of Congress registration
2) Notarised and witnessed lodging of your script with your lawyer (Very expensive)
This level of protection, however, only protects the script and not your central idea, because you can't copyright an idea.
What this means is that although I could write a film called "Shortfellas" about three midgets who rob a bank, there is nothing I can do to stop someone else writing a film called "Short Change" about three midgets who rob a bank, providing the characters and the story are substantially different from my script.
In the world of film there is no such thing as a "cheap" legal shortcut.
The real question is what is the real value of the script. If the script is the next hot hollywood blockbuster then potentially it's worth hundred of thousands, but chances are that it's not. So the real question is, is it worth the $30 to ensure that it's properly protected.