That would be an interesting question, and maybe illuminating of the general knowledge about microscopic processes back then. Some cheese, of course, has bacterial cultures involved in the making of, and so some cheese is alive, by some definition. In the usual case, though, I guess it is adding acid to milk/cream and letting it coagulate into curds and then pressing it; so the answer is probably mostly no, if we assume a relatively clean environment for making and storing the cheese. But, perhaps the writer of the marginalia is wondering if it is a process like making beer, or other fermentation that is actually using live cultures (I don't know how well the "liveness" of yeast and other cultures was understood back then; though I suspect they understood it better than the average modern non-baker/non-brewer, since so many people made their own bread and beer).