I cycled from the Adriatic to the Black Sea, crossing the Danube twice. The cycle path mentioned is not complete, indeed sections of the Danube have no accompanying road at all. However cycling through all these countries (I did not enter Serbia) isperfectly possible, indeed may be a more peaceful way of seeing them, since trouble tends to focus on more usual places and modes of transport used by tourists, such as train stations. Traffic is hardly a problem as long as the main truck routes are avoided. Just be prepared for the abrupt transition in standard of living - and even availability of supplies - upon entering Romania. I highly recommend the trip.
Fionn Petch