Could they have made the attempt? Sure, but it would have been unlikely in the extreme to succeed or to avoid an overwhelming response from the Royal Navy.

The Falklands were simply too important to the Empire as an outpost and safe harbor in the South Atlantic to be ignored or their loss accepted. Ships routinely patrolled the South Atlantic and a sizeable force was never more than a few weeks away, one that could isolate the islands from resupply, bombard shore positions, and protect a counter landing as needed.

We can look to the British response to Spee's German Asiatic Squadron to see how quickly and forcefully the fleet could concentrate to the South Pacific. After Spee's destruction of Craddock's British squadron at Coronel the Admiralty acted swiftly to reinforce the theater, An older battleship, the Canopus, that had survived the defeat was run aground at Stanley to act as a temporary floating defence battery. While a squadron of battlecruisers detached from the Grand Fleet came south. The Invincible and Inflexible reached the area in about a month and formed the centerpiece of a new South Atlantic Squadron that would defeat Spee in early December 1914 when his force attempted to move on the Falklands. While the battlecruisers were recalled home many of the smaller cruisers would spend several months in the area hunting down the remainder of the German squadron in the area into the Spring of 1915. With ships patrolling for German commerce raiders through the rest of the war along with escorting convoys.

That Spring 1915 date is important as it does mark an important shift though. As that is when Argentina finally took possession of their pair of Rivadavia class battleships that had been built in the United States. While the ships were fine examples of the first generation of dreadnoughts, they were rather behind the latest ships the 2nd generation Super Dreadnoughts, and even more behind the latest evolution represented by the British Queen Elizabeth's then coming on line. They were also notable for less than reliable powerplants leading even to engineering casualties during their trials. But they were still the largest warships from mid 1915 on that were stationed in the South Atlantic. They were backed up by some armored cruisers then that were nearing 20 years old and a gaggle of destroyers and torpedo boats.

Its certainly theoretical that a task force could have been assembled to take the islands but the British had also demonstrated they were willing to risk even their strength in Home Waters to bring overwhelming force to secure the islands from any threat.