Do I need an Apple ID to use an iPhone?  Technically no.  But an Apple ID is just an email address and password protected account that allows you to access all the features of your phone, (Apple Pay, Music, messages, etc, etc.,) so if you don't have one, one would really question why you would want an iPhone to begin ...

If you see No Service or Searching in the status bar on your iPhone or iPad (Wi-Fi + Cellular), your device isn't connected to a cellular network.