Yes, you can. Up to and including the 2021 version, you must first export the route and then email it to yourself. When opening this email on your phone or tablet, you will see the option to open the route in the Nautical Maps app. In addition, you can also email a route from the app to yourself and then import it into the software on your PC.
From the 2022 version on, routes are stored directly in your Nautical Maps account and synchronised on your devices, and thus can be used from any device.