I am not sure what Unity does, but when Z objects are the same, the drawing order seems to be platform specific rather being random.
I had a button that once pressed, spawned several other buttons which popped out from behind the main button, but on the Mac, iPhone etc they always appeared on top of the main button. The issue being both sprites had the same Z.
However the issue seems to be made more complex when you have multiple Atlases. You're probably (and quite rightly) using an Atlas for your font and another for your menu gfx. Problem is, staggering two buttons over each other will result in the text appearing over both buttons, even if the Z position and DrawingOrder is correct.
All it takes for example is one label to be really far away from your camera to make all your text vanish behind your gfx. Which can and often will be ok in Windows but not on iOS or vice versa.
Unless you use a separate UIPanel to make an extra DrawCall.
For now, my advice is that you double check your menus on your target platform every now and again to make sure you don't have any weird vanishing graphics issues. If like me you tend to copy and paste your widgets around, it can be a pain to sort out all your Z issues later.