So, after about 4 hours of trawling the web, I could find NO way to hide MagicJack on a mac! Due to the extremely annoying nature of it popping up, I absolutely HAD to find a solution... and thus was born THIS APP. I claim all copyrights on the program, however it is freeware for you to download and use. It is not perfect, but it's the best I could whip up currently... Updates may be posted in the future.
TIPS AND TRICKS
If you are a Spaces user, magicJack must be set to 'Every space', otherwise it will drag you to the magicJack space, even though magicJack will immediately be hidden
I do know that magicJack still pops up for <1s - this is unavoidable. Luckily, when it re-hides, the previous application will resume focus - full screen applications should still be in full screen mode as well.
To stop auto-hiding, you must click on the program in your dock, then click 'cancel', and then 'quit'.
I welcome all tips and tricks on other methods that will make this work better, if you know any... No, I'm not posting the .sh file that the app is using, but it's fairly simple, using osascript, and then platypus to make the .app bundle.