While it is not possible with our current technology to download complete modules, access to the LMS with train broadband (often 1 Mb or so) should not be a problem.  Try it. And remember that our Lessons have ‘full resume’ that means that, should you lose connection, you can pick up exactly where the lesson stopped when you went offline.
I think you’ll have no difficulty taking lessons, including quizzes, on the train.  However, when taking exams, make sure you have good stable broadband connection.