Can I download MAC Software onto a Linux Computer?

So a couple months ago I bought a computer and it came with Linux software. I love Linux and how free it is, but I'm having issues with iTunes and being able to connect my iPhone to iTunes. Since Apple doesn't even have an iTunes which is downloadable onto Linux I had to do it via wine and PlayOnLinux but even then I can only get an old version which doesn't support iCloud. When I plug my iPhone into my computer it isn't recognizing it what so ever, and it will not connect to iTunes. If anyone has a solution for this then please let me know.

However, this is my main question. I used to have a Macbook and I got MAC OS X Snow Leopard system with it and I still have the download disc of the software. I was just wondering if I put this into my Linux based computer will the software run and will it work okay? I don't want to do it in case it damages my computer and is unable to run as the computer is new. Does anyone know if this will work and if it is worth doing? If there's any steps that are best to take? Etc.

The computer I have is hand built by a computer specialist - very good computer. It came with Linux Ubuntu so that I was free to do or download whatever. I know that apple are really funny and can be dodgy about where their stuff will work and where it won't, hence the question.

If you are talking about the OS itself, maybe. Google "hackintosh" and read up. Your computer might support it.

If you are talking about applications, maybe. OS-X is a version of Unix, and virtually any Unix program can be made to work on Linux (if you have the sources). However, there probably already are Linux versions of those programs, so look around on the Internet first for whichever programs interest you.