Satellites weren't what they are today (they used film cameras and dropped the camera rolls onto the surface), but that would have been discovered, if anything, but some of the locals that happens to wander in a supposedly uninhabited part of the island that's suddenly crawling with soldiers. Maybe an airstrip long enough for fighter jets could have been quickly improvised in a previously surveyed site... but at that point, you may as well invade East Falkland and build the airstrip there, or prolong the existing one.
It may have worked before satellite recon at all, and best if done before the islanders got access to short wave radios, but at that point in time, the balance of powers tilts too heavily for the British.
On topic:
Thatcher falls, this may have effects on the rise of neoliberalism and globalization or it may just delay it.
If the UK contests the invasion and Argentina still win (let's roll with it as per OP), the Argentine armed forces would still have been taken significant looses (specially in the air) and wouldn't be able to immediately invade Chile. The Latin American debt crisis still hits in August, further complicating additional wars. If Argentina wins because the British don't show up, a follow up invasion of Chile in summer may be planned, but with the economy going to hell anyway, it's unlikely to happen.
The Argentine survives a bit longer, but I think it would fall before the middle of the decade anyway. There are no trials for the crimes of the dictatorship, and the military may remain a political actor in the country, not unlike Brazil. But with the fall of the USSR and American hegemony in the 1990s, Uncle Sam turned to preferring friendly/cowed democracies than military dictatorships in the region. If/when a significant economic or political crisis happens (as the OTL 2001 crisis), people may still demand a military intervention, but if the military obliges, I don't see them sticking around. They'd remove the president and call for new elections.
OTOH, depending on how the war (or if there is a war) develops,
Colonel Seineldin may become an important political figure in Argentina. His anti-American views wouldn't match the era of the USA as the only hyperpower, so if he ends up becoming president of the country (even or specially so if he gets elected to the position), that's going to sour US-Argentina relationships. On top, a victorious armed forces are going to continue developing nuclear weapons. Since satellite recon wasn't indeed what it is today, it's possible that the CIA misses the project entirely (they were taken by surprise when Alfonsin made public that Argentina had been enriching uranium for years) and the program is announced when an Argentine nuclear weapon is tested. That is not going to make the Americans happy, to say the least.
So we end up with an Argentina that's still in economic trouble, but is far more arrogant, may not be willing to join the Washington consensus, probably nuclear armed and generally acts like a stone in the US' shoe. At the time when the USA didn't have any sort of rival Argentina could lean towards to balance the scales.