Let’s look at what actually took place. We will start with the Rio Pact in 1947. This agreement bound many Latin American nations to the US in terms of defense, theoretically. But even long before that, the Monroe doctrine and Roosevelt Colliery had made the US the dominant force through out the Western Hemisphere. But the US didn’t run them like the USSR ran the Warsaw Pact. Yugoslavia by the way, was not a member of the Warsaw Pact and was a founding member of the non-aligned movement. It was also never invaded.

The concept of the third world, which is problematic unto itself, was/is composed of the developing nations not in NATO, the Warsaw Pact, nor a part of Communist East Asia. Latin America was major center of this. There were “client” states of the US and USSR spread through out the third world. Chile, Brazil, and Argentina could all be called US client states, depending on American military hardware and support. Meanwhile, Angola, Somalia (prior to the Ogaden war), and Ethiopia under the Derg could be called Soviet satellite states. Cuba, Mongolia, and Afghanistan definitely could be called client states of the USSR.

Now let’s get back to could the Latin American states under heavy American influence in the Cold War be called satellite states? Sure, because the term is subjective. The US and Soviet Union backed different regimes, like India and Pakistan, solely because the other backed its nemesis. Was Pakistan more “pro-western” than India? Probably not, but the US backed Pakistan because India had close ties to the USSR.

A thread to consider looking when considering this question is Why did the US overthrow so many democratically elected governments in Latin America?.

I suggest that, because when we think of the CIA manipulating governments and sponsoring coups, it's important to remember that the U.S. and the CIA heavily influenced and invested in the degradation of leftist actors mostly through supporting right-wing domestic actors.

As /u/iconicjester puts it, "In each case, domestic actors were the prime movers, right-wing factions within the countries themselves looking to take power and change the ideological direction. But the US was nevertheless instrumental in providing support and coordination for these regimes, and of course they were recognised [sic] rather than made into pariahs by US diplomacy."

This is an important consideration on this subject because a satellite state shares allegiance with a larger state. The question is whether these Latin American nations more aligned with the United States, specifically, or more aligned with anti-Communism and anti-Leftism irregardless of the U.S.

Despite similar results - a right-wing dictatorship that used state sponsored terrorism to combat leftist activists and opponents - most of these countries had varied paths toward that result.

Taking the example of Chile: even before the election of Salvador Allende, domestic actors felt worried about the rise of leftism. After his election, many of these actors coordinated right wing resistance and protests, from the March of Empty Pots and Pans in 1971 to trucker strikes and radio seizures by far-right movements and leaders like Carmen Saenz de Phillips.

All of these had traces of the U.S. influence in economic actions such as the CIA giving money to some of the pots and pan protestors. But it wasn't inevitable that Pinochet and the military would lead a coup - a result initially loved by Nixon, but a result not planned or executed.

It should also be noted that while the United States influenced these affairs, other anti-Communist and "Western" countries like the United Kingdom supported Pinochet and right wing movements.

Ultimately, Chile had a government friendly to the U.S. that shared common interests, but a government that also didn't follow the U.S.'s interests wholesale. Pinochet ultimately didn't reverse the nationalization of copper that Allende had commenced to the chagrin of private business interests outside of Chile. And while the U.S. supported Chile under Pinochet, that relationship grew strained from both sides through the Letelier Affair and the 1980's when Reagan and his State Department began to nudge Pinochet towards democracy.

I would argue, then, that while Chile benefited from U.S. influence and investment, the coup ultimately served a domestic self-interest against Communism with domestic actors leading the removal of Allende.