No. Reservations are separate from the app and there is no connection between them.

For compulsory reservation trains you need to have either printed or be able to show the reservations on your phone as well as your pass.

On non-compulsory reservation trains they are generally just for your own benefit to guarantee your seat and train staff will just want to see your pass.

There are many places to get reservations other than the Eurail website, often these are cheaper and better. see this thread for details.