Why Admiral Graf Spee had no safe breakout

Could Admiral Graf Spee have reached a safe port or Germany if British deception had failed?

No; the cruisers outside the River Plate were backed by Ark Royal, a battleship, and further interception forces.

Cruisers waiting outside the River Plate were only the first layer of the British response. HMS Ark Royal and a battleship were already moving toward the area, with additional forces behind them. A breakout therefore required the German ship to evade or fight through several successive interception forces while already damaged and alone. The answer treats escape as unrealistic without an impossible intelligence advantage such as satellite surveillance.