In the "phone update" section of my settings there is an option to "automatically download updates if my data settings allow it". How does it determine if your data settings allow it? By your data limit in Data Sense?
From How do I update my phone software? at WindowsPhone.com:
Updates won't download if data settings on your phone prevent it. For example, both Data Sense and Battery Saver can limit how your phone uses data. To learn more, see Using Data Sense to manage data usage and Battery: making it last. (Not all mobile operators offer Data Sense.)
The way I understand this, the "data settings" part refers to background data, which can be restricted by both Battery Saver (e.g. when battery level falls below 20%) and Data Sense (e.g. when you're roaming or near your monthly limit).
If you want to be absolutely sure that an update will be downloaded and installed successfully, make sure your phone is fully charged (or connect it to a charger), and use WiFi instead of mobile data.