I think this can certainly be a useful way of thinking about Marxism if we begin with a particular understanding of language.
Marxist linguist Valentin Volosinov argued that the sign is "an arena of class struggle." I think what he meant by this is fairly straightforward and uncontroversial: when there are political controversies about language, those controversies are in some sense expressions of class struggle.
From this conception, it follows pretty directly that the side you take in political controversies over language will often be the side you are taking in the class struggle. As a trivial example, we can probably infer something based on whether you think the rich are better described as "job creators" or "parasites". What's telling is not that you have picked words with particular definitions, but that you have picked the same words that the working class has picked, and in opposition to the words that the bourgeoisie prefer. I don't have to even speak English to grasp the essential class dynamic here; all I need to know is that there's a class struggle over which word to use, and who is advocating what word.
In that sense, Marxism certainly can be defined as a speech community - specifically, the community which sides with the proletariat in linguistic class struggle against the bourgeoisie.
This is easy enough to see in controversies like the one mentioned above; but of course, in more complicated or subtle controversies, it's not necessarily clear which side is aligned with the interests of which class. When self-identified Marxists disagree with self-identified Marxists about what Marxism is, and when that disagreement is expressed as a dispute over terminology and language, the notion of Marxism as a speech community stops being useful. Linguistics gives us no insight into the conflict; the sides may very well be aligned with opposing class interests, but nothing about the language they're using tells us who is who.