I've been giving some thought about this recently. I'd say that, at least for software, we'd still need the GPL and, therefore, copyright. Which clashes a bit with my anti-copyright sentiments, but whatever.
Why is this? Because software is different from literature and visual arts. In a copyright-free world, once you copy a work of literature you have the whole work at your disposal to copy, modify and redistribute however you see fit. For music it's a bit different because you may need to reverse-engineer the music sheet, for example, but there's a lot you can do with just the recording of a piece of music.
With software, the only thing you could do is copying it, or try and modify the binary, because you still don't have the source code. Sure, you can reverse-engineer it (which is already legal in some situations in certain jurisdictions), but the software wouldn't be free in today's understanding of what many consider free software (i.e., software that respects the four freedoms outlined by the fsf). This means, you get your copy of, e.g., AutoCAD, but it would still be hard for you to modify it, because, despite the absence of copyright, you'd still have no way of getting source code to work on (unless someone leaks it).
So I'd say that, at least, absence of copyright wouldn't help with software. It will just create a situation where those who want to incorporate your source code into their products without publishing their source code will be able to do just that, and you'd have no recourse.