Would I need to have a SIM in my phone to update iOS over the air?
Often, an iPhone will refuse to function in there is no SIM present. However, I have found that if your iPhone is active, and configured, you can use it and update, OVER WIFI, without the SIM card.
By active I mean that the phone is configured with your information, and set up and running. So, in this case, the phone was being used, and you removed the SIM card to say place in another phone. In this case, yes, you can update the iPhone over Wifi. However, if the phone is not activated, and you have not configured it, the phone will refuse to move forward in the configuration process without the SIM card.
When trying to activate your iPhone, a message might say that your iPhone cannot be activated because the activation server is unavailable, the SIM card is unsupported, or activation couldn't be completed. Follow these steps.