Not at all close. I wrote a short history of the Italian communist party here which you might be interested in, as well as this older answer about the Italian Communist Party's complicated relationship with the Soviet Union.

After the Second World War, Italy was occupied by the United States. This alone was an enormously influential factor in determining the country's post-war alignment. While the Soviet Union led by Stalin had acted quickly and decisively in order to prop up sympathetic governments in newly occupied territories, the United States' presence in Italy meant Italian Communist Party (however instrumental it might have been in the resistance to fascism) could draw on no analogous support. However, we could still ask how close the Communist Party, working with its close ally the Socialist Party (the distinction between the two was, in the immediate postwar era, more a question of personal relationships than anything), might have been to autonomously instilling a Soviet-leaning government capable of forcing through an adherence to adhere to the Warsaw Pact. The answer, however, is still "not very close at all."

There was, on the one hand, an active courtship of the United States by the nascent Christian Democratic Party: Christian Democratic mandarin (and later Prime Minister) Alcide De Gasperi had exploited his post as Foreign Minister under the king's rump state in order to build a strong relationship with occupying authorities. De Gasperi was able to bring occupying authorities' attention to the uneasy hypothetical of communist revolution, and this dialogue had the added effect of elevating the status of his own party. The Christian Democrats were further strengthened as they emerged from the final phases of the war as important social and economic brokers, since as early as the winter of 1943-1944 wartime pragmatism led the United States' State Department to shift its policy of economic relief to one of outright industrial rehabilitation, with Italian resources commandeered in order to fight up the peninsula against the occupying German forces.

On the other hand, the United States government was much more hands off than it Communist rhetoric would later accuse it of being. Once the war was over, the policy of choice became one of guarded indifference, albeit with general sympathy towards the Christian Democrats and distrust towards the Communists and Socialists. But material support to the Christian Democrats was ultimately negligible, and as much was seen in the results of the election for the constituent assembly: a strong performance in rural communities and among small-town bourgeoisie saw the Christian Democrats get 35% of the vote, but in the country's large cities the haute-bourgeoisie was handily outnumbered by working-class voters, and combined Socialist and Communist lists beat out the Christian Democrats with 38% of the national vote.

The wartime memory of the partizan militias, many (but not all) of whom were declaredly Socialist or Communist, was still fresh in Italian political dialogue: the urban working class (and people in any area of the country which had seen significant military action) identified in the partizans guardians against fascist oppression, while the bourgeoisie rather less enthusiastically saw in them an armed and dangerous force poised to turn on them at any moment.

But was there a gap between memory and reality? Given their numbers in the Constituent Assembly, excluding the Communists from the constitution-writing process was impossible. But the constituent assembly also appointed the country's government, and while the first three cabinet reshuffles featured Communist participation, by the spring of 1947 recognition of the communist's social and political power had declined to the point that the Christian Democrats constructed a communist-proof majority to carry them all the way to the following year's election. Clearly, as early as 1947 there was no realistic worry that the Communists would take up arms again. So there indeed seems to have been a gap between perception and reality as concerned the communist partizans (and the Christian Democratic leadership knew this). In fact, the communist militias had not even been alone in their opposition to Fascism, as throughout the final phases of the war they had counted on catholics, dissatisfied fascists, and all a manner of opponents to the regime among the partizan ranks. They also could count on the collaboration of local administrations as well as local citizens for material support. Lastly, their effectiveness was amplified by the slow but steady progress of allied forces up the peninsula, draining military resources from the internal defense of cities and towns behind the front line. So while the memory of antifascist militancy was still fresh in the 1948 election, it was still three years after the war's end both Christian Democrat and Communist leadership recognized that none of these factors would manifest to help them should they again take up arms and push for a coup.

As tensions nonetheless ran high in the 1948 election, what would have happened if the communists had indeed taken up arms once again, this time to force electoral results their way via violence and intimidation? As already stated, now that the country was rid of the yolk of fascism, the communists would have to make due with a much reduced pool of allies willing to take up arms along side them. But would even their staunchest supporters have the energy to halt the country's reconstruction process and interrupt the peace which had, by now, reigned for the past three years? Probably not, especially since many among the urban working classes were still unhoused and unemployed. The Communists could, hypothetically, foment some sort of conflict or crisis with a goal to ask the Soviet Union to intervene by force of arms (as the soviets had done in so many countries that constituted the Eastern Block) but the Soviet leadership was far too taken with steeling their grip in the countries which they already occupied, and were in no position to intervene in Italy (subject, as it was, to an enormous American military presence which would last throughout the Cold War). So not only were the Communists on their own, there was also no indication that there was ever any threat of Soviet intervention in Italy even when relations between the Soviet Union and the Italian Communist party were as strong as they were in the late 1940s.

It is nonetheless undeniable that many (if not most) the leaders of the Italian Communist Party in the late 1940s were in communication with the leadership of Soviet Union, regularly traveled to Moscow, and participated in international conferences and events organized by the Soviet Union. But what this line of communication and dialogue achieved, beyond visibility in media and in international politics, is ambiguous (in spite of accusations claiming otherwise by political rivals). These achievements would also pale in comparison to the capital investments brought about by the Marshall Plan and IMF loans, which the United States' leadership provided as a macro-response to slow postwar recovery and deteriorating relations with the Eastern Bloc. However, even this high-profile support was only ever dangled before De Gasperi and the Christian Democrats as reward for a communist-less governing coalition emerging out of the 1948 election, thus leading the Christian Democrats to do their own dirty work. It's true that in response, communist members of parliamentary commissions were later able to broker high-profile agreements between Italian state-sponsored companies and the Soviet Union, but the impact would nonetheless never compare to the aid that the Christian Democrats had brought home from the United States.

The only path for Italy to join the Eastern Bloc would be through fair electoral victory. But history would show this was impossible: even though the Italian Communist Party remained a powerful political force, there were never the conditions to appoint a communist-led government. This of course didn't mean the Communist Party wasn't an important political player, as throughout its life the party represented millions of working-class Italians, provided the loudest electoral alternative to the conservative politics of the Christian Democrats, and even proved itself capable of begetting popular and capable administrators in those local governments where it was able to wrest a majority. The party also proved capable of evolving over time, housing a multitude of differing factions and currents: some of these were pro-Soviet; others professed themselves faithful to the original ideals of communism; and others still presented a new and wholly Italian take Communism. But all this meant that even when in the late 1970s conditions again existed for the Italian Communist Party to discuss joining the governing coalition, adherence to the Warsaw Pact was not even a policy item on the table (in fact, the official party line had become sympathetic to NATO).