The answer is obviously 'no,' but I think there might be something to this question, as I remember several Chinese-American friends having told me as much when we were growing up. My hypothesis is that they meant to say 'facetiousness' rather than sarcasm.
I teach Shanghainese 18 year-olds classes on irony and satire, which they uniformly call "sarcasm" because the Chinese word 讽刺 is used for all three. My students definitely understand sarcasm-- barbed insults often formed by stating the opposite of what is meant.
However, Chinese students are not introduced to forms of irony wherein the purpose is not specifically to mock or lampoon something. This is not to say that Chinese culture has no history of it, but more that the humanities (including critical examinations of Chinese history and literature) are less emphasized in the Chinese education system relative to western ones. Specifically, it's possible (and probable) that one could graduate from an elite university without ever having studied literary irony. For perhaps obvious reasons, the ruling class don't particularly care to encourage it (there is now meant to now be a ban on making puns in broadcast communications).
I teach lessons on understanding Onion articles, and I don't believe there is any Chinese analogue to that sort of open-ended satire. It is the first time that my students have encountered anything like it, and they typically have trouble understanding why it exists (as, no doubt, many westerners would as well). Their question is typically "who exactly is this supposed to be mocking?", and they have trouble understanding that the author is encouraging the reader to ask certain questions rather than guiding them to ridicule someone. To be sure, there are significant cultural obstacles to understanding satire, but my students are unfamiliar not just with the references, but with the entire genre and its purpose. Another example is Body Ritual of the Nacirema, which contains few cultural references that Shanghai students wouldn't get, but which has no specific target. Most students get lost trying to work out who is meant to be the object of ridicule, but the purpose of the communication goes beyond that.
But aside from obscure literary styles, I think it *might* be the case that the Chinese tend to be less facetious than, say, the British, just as Americans tend to use less irreverent humor. Being facetious often means purposely using inappropriate diction or making extreme statements that one neither totally agrees nor disagrees with, with the purpose of calling attention to social norms that forbid taking those sorts of attitudes rather than lampooning an individual or institution. It's harder to understand than sarcasm because there is no object of ridicule and because the speaker intends neither what she says nor the exact opposite. At any rate, Chinese students are usually thrown off by facetiousness in English, as one needs to be fairly familiar with social taboos in order to find it funny.