So I thought for the fun of it @Jeremy_M I would do that to see what happens. It rolled everything back to Koodo except the cellular data. I bought my iPhone 5s outright two months ago at a Telus store.
That that was a little odd but I was on Koodo before going to public and still have that sim going in a different phone.
Great point, when you reset the network settings, it will remove WiFi and APN settings you originally had configured back to its virgin state. Therefor you are correct to say that you would have to re-configure your APN settings to work with Public Mobile.
Also @chukdefatey handsets and their APN settings are pre-configured from the mobile company you purchased your phone from. So when resetting it's goes back to factory settings.