If I used only plug-ins that work both on iOS and Android, could I achieve write once run anywhere?
For most of your code yes. Some plugins can be tricky, but for the most part of it, it's easy to use on both platforms. You will have to take care at some components too, like DatePickerIOS which have an equivalent for android, DatePickerAndroid. Sadly those 2 components don't work the same way.