Possibly, but not necessarily. If we look at the sheer number of graffiti and the fact that many of them are of vulgar (in the linguistic sense, not the weird way that contemporary English uses the word) and use those as more or less the sole criteria, sure. But there's a lot more that's implicit here than what you're suggesting we look at.

Yes, much of the graffiti at Pompeii is vulgar in nature. However, while the sensationalist graffiti with which you--and most other people on the internet--are familiar often deal with the sexual, the taboo, and the "common," that only accounts for some of the graffiti at Pompeii, and they're not even the majority of extant inscriptions. The vast majority of graffiti at Pompeii are only a couple words long, typically just names or are like CIL 04, 02227, which is just the word "Victoria" scrawled onto a wall. Many of the graffiti at Pompeii are nothing but pictures, which can be hard to track down since you won't find them in the CIL. An entire class of graffiti at Pompeii are just tally marks scratched into walls or blocks. Inscriptions like CIL 4.8185 (Mula fellaat [A]ntoni/Fortunata a(eris) a(ssibus) II, "Mula [lit. "the she-mule," obviously not a real name] sucks dick(?) [A]nton(ius?). Fortunata for two bronze asses") are not nearly as common as clickbait articles and undergraduate courses would have you believe.

Most, then, of these graffiti do not even indicate literacy at all. Since most are only a word or a couple of words, or straight up just a picture, we cannot determine whether the inscriber had a full grasp of written language, whether he or she (almost all identifiable graffiti at Pompeii are written by men, which seems relevant to the problem of literacy) had "functional literacy," or whether the inscriber was effectively illiterate but knew enough to write his name or a word or two. Of "full size" graffiti, that is those that contain full sense units and aren't just a word or two scratched onto a wall, almost all do not indicate clearly the social position of the inscriber(s). In the nineteenth century it was a common belief that the wealthy population of Pompeii fled the city after the 62 earthquake, leaving it entirely in the hands of the poor. This is known not to be remotely true now, but the evidence that scholars a couple centuries pointed to was the enigmatic trash heaps that surround the city walls, the gladiatorial riots of 59 that were thought to be the original impetus for the wealthy flight from the city, and the large amount of graffiti, which was assumed could only be the work of the lower classes.

However, when we actually examine the graffiti we find that those graffiti that might potentially be identified with a social class do not necessarily line up with the lower classes. The most obvious type of this class of graffiti is of course the electoral notices (programmata) posted all over the city, which could not have been put up by random people walking the streets. However, a large group of Pompeii's longer inscriptions is the verse inscriptions. These are a mixture of original compositions and citations of great authors. That these are clearly highly learned inscribers is probably beyond question. One graffito (CIL 4.1520), for example, famously combines two modified lines of Propertius and Ovid to create a new epigram. The inscriber must have had a good knowledge of the corpora of both Ovid and Propertius, as well as an understanding of poetic meter and style, and the skill not only to combine the two lines but actually to modify them so that they created two new lines. As if that weren't enough, the graffito is from the Casa degli Scienziati, a high-end residence in the city. Which means that unlike CIL 4.1893-1894, which similarly combines a Propertius poem with an Ovid poem in the same hand but was found on the wall of the basilica, CIL 4.1520 must have been scratched by somebody who had access to the inner areas of this very expensive house. The picture of the inscriber, then, must be of somebody closely connected to the owner of the house and very learned, whether this means he/she was a fellow wealthy landowner or a well educated client. CIL 4.1520 is not alone--a huge quantity of Pompeian graffiti is found within expensive private residences.

A particularly famous example is the collection of graffiti found on the stairwell of the House of Maius Castricius, a high-end urban residence. Here some eleven graffiti are scrawled into the same space, many of them referring to each other and the majority of them in verse. The graffiti here present an example not only of the same phenomenon as CIL 4.1520, but also an indication of something that CIL 4.1520 only hinted at. The coupling of Propertius and Ovid in CIL 4.1520 is echoed by CIL 4.1893-1894, but they're not the same poem. However, several of the graffiti at the House of Maius Castricius are identical in text, though not in hand, to inscriptions found all over the city. "Venimus hic cupidi" (we came here desiring) is found at another nine locations in the city. "Quisquis amat valeat" is found at another twelve locations. And neither of these lines stands alone, they make up larger poems that include original lines. What this suggests is that a culture of graffiti existed at Pompeii among some section of learned people. Part of this culture was the construction of elaborate dialogues, similar to those that we find on the walls of shops in prose but more closely relate to the "capping" of songs sung at symposia, in that they are demonstrations of the inscriber's education. Increasingly scholarship is finding that inscriptions at Pompeii, while not necessarily directly referring to each other, form a part of a graffiti culture that appears too elaborate and often too educated to be simply the product of random poor people walking by.

That there might be a unique graffiti culture at Pompeii is perhaps not too surprising. Our evidence for graffiti elsewhere is lacking, and cultures of public (and at Pompeii, also private) inscribing are very different across time and place. Anyone who's been to Rome will have seen, though perhaps not realized what they were looking at, cantos of Dante spray-painted on walls, and the walls around the university at Naples mix political murals, passages from Marx, insults towards the authorities, and raunchy addresses towards girls (and boys). Similarly, graffiti take recognizable forms at Pompeii, and are often quotations of other graffiti. They're also found at specific spots, clustering around shops, basilicas, the amphitheater, and private homes. The location of graffiti, and the fact that they usually come in groups, suggests that location is every bit as important in the meaning as content. This seems self-evident--the crap you'll find on a public bathroom stall in Harlem is not going to serve the same purpose as a big political mural on the side of a public building in Chicago--but it's too often overlooked by people who look at Pompeian graffiti and are amused by how raunchy and vulgar it is. The mere fact of graffiti is not sufficient to determine the social position or education of those who write it. Nor is the content of graffiti necessarily sufficient to demonstrate the same things. The Pompeian evidence on that front is, therefore, somewhat inconclusive.

One final note. I, like many epigraphers (Greek epigraphers at least), tend to argue for a much higher literacy rate than many classicists. That observation of a complex graffiti culture that we cannot really understand may be enough to argue for a more complex picture of literacy, if not necessarily proving a higher literacy rate, is perhaps best shown not by Pompeian evidence, but Archaic Athenian evidence. For a very long time the dominant argument was that Athenian literacy was unusually high, elevated by the democracy, which promoted literacy in its citizens and which employed publicly posted written inscriptions much more freely than most cities. However, around ten or fifteen years ago Merle Langdon started finding graffiti in the rock faces in the countryside way out in rural Attica from the Archaic Period. Langdon has since found more than two thousand of these things in the rocks in rural Attica. Compare that to the 11,000 graffiti at Pompeii, a much denser, more educated, more developed area and the achievement is put into perspective. Almost all of these inscriptions are written by shepherds talking to each other, and unlike Hesiod's persona that he's just a rustic Boeotian farmer these are unlikely to be a poetic persona. There are so many hands, the spots are so remote--it's hard to imagine landowning elites going out there to write their names--, and the majority of the inscriptions are just alphabets or notices of people's names. But these inscriptions also demonstrate that already in the Archaic Period at Athens there was a developed graffiti culture way out in the Attic countryside among the herdsmen, who write messages (often quite mean or sexually demeaning) to each other. The cases are not parallel, in that one is a rural society just on the cusp of literacy, whereas the other is a heavily urbanized society long after literacy had taken hold, but Langdon's evidence suggests that there is a place for graffiti in understanding the literacy of the ancient world.