Argentina can definitely take the Falklands if they attack. The Falklands and the UK mainland is 8000 miles apart; it's naive to think the 1600 odd defender (with FIDF) can cause any problem. They are going to lose an arm and a leg taking the island, and then will not have enough troops to defend against a counterattack from the UK. When they come with a shipload of reinforcement like they did back in 82.
The main issue with Argentina is that they don't have a proper Navy and their Air Force is weak; even the RN is not what they used to be in 82. They are going to get isolated if they had taken the Falklands; their Navy would either have to fight the Royal Navy and get sunk at the bottom of the ocean, or they are going to do hit-and-run, which means limited supplies onshore.
What the Brits did with the Falklands now is what we did to Midway back in WW2: there are no way we can defeat an oncoming Japanese attack; we can take away their supporting element by taking out their Navy, then their troop; even if they can make it ashore will be doing nothing.