There may be circumstances where you may want to watch a rented movie on your iOS device where you have no WiFi or Cellular Data connection (e.g. on a flight or in a remote area). Apple’s official documents state “an Internet connection to the iTunes Store is required to authorize playback.” So, the question is whether an internet connection is required to watch a rented movie?
The answer is simple. The authorization takes place when you download the movie. Watching the movie does not require an internet connection.
So yes, you can watch a rented movie from iTunes without an internet connection
But you need to download the movie to your iDevices before watching it. At that point, you have 30 days to start watching that movie, once you rent it.
And be mindful, that once you start watching the movie, you have just 48 hours to finish it. You can watch the movie as often as you like until it expires 48 hours later.