Even though Renown and Ark Royal were a thousand miles away, it’s doubtful under any circumstances that Graf Spee could have escaped to see home waters again. The long battle of the River Platte must have seriously depleted her shell rooms, so it’s doubtful she had the ammunition to engage in another long stand-up fight. Even though she’d knocked HMS Exeter out of action, Exeter had been replaced by HMS Cumberland, another 8” gun cruiser. Thus, the British would be about where they were when the engagement started.
The real liability Langsdorff had was a lack of speed. As Graf Spee could only make 26 knots, she could never outrun the British cruisers. HMS Ajax & Achilles (Leander class light cruisers) were capable of 32 knots. HMS Cumberland (Kent class heavy cruiser) was capable of 31.5 knots. So Harwood could have elected to simply shadow Graf Spee until Ark Royal and Renown arrived. Renown, a 32,000 ton battlecruiser with six 15” guns and top speed of 31 knots, would have made very short work of Graf Spee. In fact, the destruction of armed commerce raiders such as Graf Spee was exactly what Renown was designed and built to do.
The interesting “what if” here is whether Renown would have gotten to fire on Graf Spee at all. It is possible that Ark Royal’s swordfish torpedo planes would have sunk Graf Spee in an air strike. If so, Graf Spee would have been the first “capital ship” sunk by aircraft during wartime. Much earlier than the Italian battleships at Taranto (also by Ark Royal), much earlier than American battleships at Pearl Harbor. Most important for naval history enthusiasts, she would have been the first capital ship sunk while underway, instead of HMS Prince of Wales and HMS Repulse on December 8, 1941. It is important to note that until the loss of HMS Prince of Wales, it was generally accepted that while under way and with AA defense, a capital ship would not be sunk by an air attack.
It would be interesting to see how differently naval strategy would have evolved between 1939 and 1941 had Ark Royal planes sunk Graf Spee.
IIRC, Langsdorff thought the Renown and Ark Royal were already on station and waiting for him to try and break out. But you are correct, he would never have made it home. The Royal Navy would do whatever it took to sink her.
They fought and they fought to win.