Could Scharnhorst and Gneisenau have survived Rodney?

Was it reasonable to believe Scharnhorst and Gneisenau could not survive an encounter with Rodney?

Yes. If Scharnhorst and Gneisenau could not escape by speed, Rodney is judged certain to win, particularly with Renown present.

Scharnhorst and Gneisenau normally possessed the speed to refuse combat with the slower Nelson-class battleship. Renown changed that geometry because the battlecruiser could keep contact and force the Germans to maneuver under fire. If damage reduced their speed, Rodney could close and bring a much heavier battery into action. The judgment is firm that Rodney would win if escape by speed became impossible. Lütjens's fear followed from the consequences of losing that advantage.