I know you didn’t ask me but, If I could have set up a rondezvous with a supply ship, with food, fuel and ammo (although I am pretty sure the GS had plenty even after the fight) and had enough food and fuel to make that rondevous then I might have risked making a run for it, at night, trying to avoid a general fight. Get past the cruisers, try to out run them and lose them if possible. But it would have been difficult and all the cruisers had to do was shadow. German (or even Spanish) ports were awfully far away. And eventually something bigger would show up if I couldn’t lose them.
If I could not arrange the resupply then no, it would have been a waste to even try
and ship’s captains rarely make suicide charges…some do but not most. A ship would have to have a decent shot at making some friendly port.
And the River Plate while wide at its mouth and looks very big in maps/photos (Montivedio is on the big entrence) is not a very manueverable body of water, (we were in port at Buenos Aires once) you would be forced to stay in the channel for quite some distance and given how the Brits fight they probably would have violated the soverignty and fired on the ship in the channel. Who knows?
I spent 6 years at sea and any sailor with an ounce of salt learns to respect the power and danger of the seas. Sailors have two enemies, the other guy on the other ship and the ocean. Get beaten by one and you might not (if they don’t pick you up) survive the other.
German ships did elude the British Radar many times during the war, not sure if any of these ships had it.
You know the more I think about it making a run was probably, given the cirumstances, not a good idea.