Tracey Lien from Polygon reports that Crimson Dragon will feature a free flight mode, alongside the on-rails mode:
The game will also have an on-rails mode and a free flight mode so players can decide how much control they want over the movement of their dragon. We played the on-rails demo but were still able to determine where our dragon moved with the left stick while aiming with the right stick.
It is not clear what the free flight mode entails beyond this, but I’m hoping for the option to explore Crimson Dragon’s levels with free roaming controls after they’ve been completed, similar to Panzer Dragoon Saga’s flight mode outside of battle.
The article also explains how the asynchronous multiplayer works when your friends are not available to play in real time:
[P]layers will be able to take part in real-time multiplayer battles with friends or they can play with the dragons of friends who are offline in the asynchronous mode. The game will support Xbox Live friends lists and, if players don’t have any friends, they will be matched with strangers.
I’m looking forward to playing alongside some of you, be that synchronously or asynchronously.