Not exactly, Khar. At root, intellectual property over copyright (as opposed to trademark and patent which are very different situations) is the creator's right to control the performance, reproduction and distribution of their creative expression. As a musician, it is what prevents another person from hearing the song you wrote, performing it and claiming it as their own, or recording your song and selling the recordings for profit at less than you are charing for your own recordings. Were people able to do both these things without repercussion, it would be far harder to earn a living as a musician.
In answer to your question, Damnable Fiend, copyright regimes change from country to country although most first world countries have broadly similar regimes that are coordinated, in a general sense, through international treaty. In Canada and the United States your copyright attaches to your song composition as soon as you write it (giving you certain legal rights to prevent other people from performing it without your permission), and to your song performance as soon as it is performed (giving you certain legal rights to prevent other people from recording it without your permission, or copying your recordings and selling them without your permission).
Therefore without anything written down, in Canada and the United States you have a legal right to "enjoin" (sue to legally prevent) someone from breaching your copyrights in your compositions and performances, and you may sue for damages if they have already breached the copyright, by, say, recordings your performances and selling the recordings online without your permission. However, just because you can sue, doesn't mean it will be easy to prove that the composition was your composition, or that the performance recorded was in fact your performance. In an actual lawsuit, there are several steps that you would have to take to make this proof, which I could go into at length but won't. Otherwise this post will be really, really long.
Now, in both Canada and the United States there exist regimes where you can "register" a copyright. This sometimes confuses people into thinking that if you haven't registered a copyright, you don't have one. Not true! Again, the copyright attaches automatically as soon as you create the composition and perform the performance. The point of registering a copyright is "evidentiary", meaning that you are now in a database publicly claiming something as your own, and this makes it far more difficult for someone else to come along and say "hey that was mine!" It's still possible for this to occur however. For instance, it is not unheard of for someone to plagiarize something and then register the copyright to make it difficult for the true author to assert authorship. These situations tend to get ugly.
Where the importance of writing comes along is that, per Tommy's article, the United States copyright law limits the transfer of copyright by oral agreement. Normally, if I create a composition and then perform it, I can sell to you all my rights to perform the composition, record the performance, sell the recordings, etc. So you give me money, and in return, it's like I never created the composition at all (with a few little exceptions that I'm not going to go into). Now if I were to try to perform or record and sell recordings of my own composition without your permission, you could sue me. Generally when you hear about musicians get fucked by their labels, it's because they sold all rights in their compositions and later found out that they had received far too little. However, per the article, that agreement that we make to sell the copyright from me (the musician) to you (the buyer) has to be in writing. In part, this is to prevent some unscrupulous person from lying and saying that we had an oral agreement to sell the copyright when in fact we did not.