Doing the same as in voting for Mussolini? Or supporting his government?

It's a tricky thing to say that no one did something. And I'd like to check Chomsky's argument because the idea sounds more from the 1930s rather than from the early 1920s in Italy (or, is he talking of other left wing intellectuals?).

The idea that the explication of the most direct, blatant and crass forms of political authoritarianism would reveal to the masses the true nature of the capitalistic system and, in substance, dispel any delusion of cooperation between the proletariat and the "moderate" wings of the bourgeoisie for a policy of social reforms, has its own history that I don't think I can pin down on general terms. Since even within Italy it is closely tied with debates over parliamentarism, representation and the nature of legal (and illegal) political organization.

Now, that's more a thing for countries where you can vote, where you can be a socialist representative, where you can legally form a political organization. All possibilities that were conspicuously absent from Italy in the 1930s - which is around the time where the view that Fascism (the "extreme reactionary form of capitalism" - as I am sure someone called it) could teach the masses a good lesson on the surface nature of those ideas of cooperation, representation and social advancement, became somewhat popular.

This idea would play some role in the so called "strategic abstentionism" position assumed by certain political forces after 1945 (and in part to mark a distinction from the official position of the PCI) but was far less meainingful in 1919, 1921 and 1924. The three elections where someone might have voted for Mussolini.

In part, there was no need to teach the masses a lesson about the dangers of the capitalist system, since there was already a gold standard for "see what collaboration with the bourgeoisie brings you" (even for the current US President, the Great War with its almost 600,000 dead and close to 900,000 invalids within Italy, would be a very high bar to get reach) - which is to say that in 1919-20 the "maximalist" position, advocating at least in theory for the Bolshevik revolution, the socialization of land and factories and the proletariat dictatorship was the official line of the Party of relative majority within Italy (156 seats over 508). It's highly debatable that the party direction had true and substantial revolutionary designs - or that the affirmation of the fraction which did was at all possible - but, at least on the surface, the lesson on the non-cooperation with the bourgeoise governments had been accepted.

It is true that the inability of the Italian Socialist Party to rid itself of the reformers stimulated the division from the Communists in 1921 - but then, again, the Communists took part to the 1921 and 1924 elections with their own, real, candidates and, especially in 1924, with considerable personal risk.

There is no reason therefore to imagine a vast movement in favor of voting Mussolini, as the worst possible choice. And it is highly debatable that Mussolini could be regarded, even in 1921, as the "strong-man of the reactionary bourgeoisie" (even if the fasci had taken up that function already within the agrarian regions). Most of the Italian political world appeared to look at Mussolini as a possible moderating force in the ongoing social conflict, and the man who had a chance to institutionalize the fasci after the PNF had "assumed the leadership of the national anti-revolutionary movement", to cite from the 1924 publication from the Institute of Statistics. The Socialists and Communists might have disagreed on his moderating function, of course, but it would be quite extreme to assume that they regarded him in 1921 (or even in 1924 to an extent) as the expression of a different surface-form of capitalistic organization.

His election to the Parliament in 1921 took place in Milan, where he led the National Block - and gained a total of 194,670 preferences - with its seven elected representatives. The Official Socialist Party was still by far the most successful in town (even if Mussolini had vastly improved from his 9,064 of 1919) with 14 elected representatives over 28 seats available - led, as usual, by the reformers Turati (300,157) and Treves (293,270).

From there, when he was appointed Prime Minister in 1922, the Fascists counted on an alleged 36 representatives over a total of 535. His election was never in doubt, nor his appointment depended on the amount of votes he received, so that the specific argument of voting for Mussolini to hasten the crisis of capitalism would have made very little sense back then.

Which isn't to say that nobody ever spoke of it. But I have no evidence of that, as of the time when Mussolini was elected. As for the Communist postion during later years, which might be what Chomsky intended, I believe it goes beyond the scope of your question - and still has very little in common with the contemporary situation you mentioned.