Not in America, though I'm less sure about Europe. Indeed, many of the earlier Marxists in American sociology, the discipline I'm most familiar with, were European emigrees who left shortly before or after World War II. Today, the sociological "holy trinity" is Marx, Weber, Durkheim, but this was a development of the 1960's, I've been taught. During the 1930's, for instance, the Talcott Parsons ruled the roost of American sociology, and his proposed holy trinity was Weber, Durkheim, Pareto.
There were certainly plenty of Marxists intellectuals in the US by the 1930's, but they weren't necessarily associated with universities, which were markedly more conservative in those days. My favorite story is that Bertrand Russell was appointed professor at CUNY (then one of the top public universities in the country) and in short order dismissed by court order for being "morally unfit".
It's also worth remembering that, among leftists, Marx and Engels were on the disreputable end. Here's a excerpt from Engel's introduction to the 1888 English edition of the Communist Manifesto:
When it [the Communist Manifesto] appeared, we could not have called it a socialist manifesto. Two kinds of people were regarded as socialists in 1847. On the one hand were the followers of the various Utopian systems, especially the Owenites [followers of Robert Owen] in England and the Fourierists [followers of Charles Fourier] in France, both of which at that time had dwindled to mere sects that were already dying out. On the other hand were the numerous social quacks who, with their various panaceas and every type of patchwork, wanted to do away with social evils without, in the slightest, harming capital and profit. In both cases they were people outside the labor movement and looked far more for support from the 'educated' classes.
On the other hand, that part of the working class which was convinced of the inadequacy of a mere political revolution and demanded a fundamental transformation of society -- that part at the time called itself communist.... In 1847 socialism signified a bourgeois movement and communism a working-class movement. Socialism, at least on the Continent, was respectable enough for the drawing room; communism was the exact opposite. Since we were already then definitely of the opinion that 'the emancipation of the workers had to be the task of the working class itself,' we could not for one moment be in doubt as to which of the two names to choose. Nor has it ever occurred to us to renounce it since then.
In Europe, I believe Marxist thought was already starting to have some influence in the universities by the 1930's, particularly in places like Germany, but it was much rarer in the United States. I can't say much about the situation in 1917, at the time of the October Revolution. Marxist thinkers from 1939 who are particularly influential among today's academics tend to be those like Rosa Luxembourg, Antonio Gramsci, and Georges Sorel who were political leaders, not academics. Besides the Frankfurt School (the first major Marxist-influenced research institute founded only in 1923), there are a few Hegelian philosophers (Alexandre Kojève comes to mind), a few artists who were not associated with universities (Bataille, for instance), and a few scattered academics here and there. Georg Lukács, for instance, was an academic and then an important Marxist thinker—but I think his turn to Marxism came after his time as an academic. Antonie Pannekoek, on the other hand, was simultaneously an academic and a Marxist political leader in the Netherlands, but I believe his academic appointment was in the sciences rather than humanities or the emerging social sciences. In short, I believe it was quite rare. Even today in academia, it's a view held by almost no one in most fields, and a small but vocal minority in most others, with it only being "rampant" in a very a few fields, seemingly.