Will a change to the Web.Config file require that I restart IIS?

Solution 1:

Changes to the web.config will trigger the app to be reloaded by IIS as soon as there are 0 connections left to the app. You can also stop and restart the app pool that the app is assigned to in order to make this happen. You do not need to stop and restart IIS itself.

Solution 2:

It depends if your application reads the configuration file every time it needs the setting, or monitors the file for changes (like log4net does). If not, you need to restart the application.
Note that by default, any changes to any file in an IIS managed folder, will usually result in a restart of the application domain.