Yes! Road Trip Maps are available on both mobile and web, although they might differ slightly. Some features will be the same, some different due to the nature of the device and setup. It's best to do the planning on a single device so that you have all the options you need. If you begin planning on one and pickup on another (ie: begin on the app and finish on the web) there will be differences to the options available for route planning.
Occasionally, upgrades in one place (ie: mobile vs web) will make things look and act different for a bit until the other is able to update, as well, but don't worry, you won't lose your trips.