Short Answer: In main Marvel continuity, No not really; May Parker's maiden name was Reilly, so by most accounts, she was born Irish-American. This has been the established norm for most of the other Marvel continuities, and May's look and persona has generally been "built" around that "sweet-natured, white haired grandmother" archetype, which would have been influenced by that background. As such, most versions of May tend to also look pretty similar/phenotypical to each other, with light hair (usually gray, white or silver) that was implied to be blond or very light brown in her youth. But generally, no, not Italian... she has been canonized more as Irish than any other ethnicity or heritage.
Detailed Answer: Because this is comic books, multiple versions of any one character can exist, but generally....all of the aforementioned information still counts. Interestingly enough though, while her family background remains the same, the factor most often adjusted for different versions of her is May's age. By most accounts, Ben Parker and his wife were already notably older (between 8-15 years or so) than his brother Richard (Peter's father). So by the time they became guardians to Peter, they were long established adults. Most versions of Ben and May were at least middle-aged by the time they took their nephew in, if not elderly. So while May's look can change--- and her persona and "sex appeal" are adjusted based on that---- she's most often an older woman by the time Peter is in his teens.
This creates an interesting issue in defining the "canon" ethnicity of the character; a person's ethnic background will naturally influence (or be evident in) their physical features, and how a character looks influences how they translate in different media. However, again... these are comic books, a media in which several different versions of the same person can and do exist simultaneously, without any being "wrong"... just "outside main continuity".
As she is based on the "caring grandmother" archetype, most versions of May are visually easy to identify; her basic outward design, (small stature, slim frame, light hair, cheerful face, friendly blue eyes)... all of which can indicate her heritage, are generally kept in tact. Usually, more superficial stuff like height, weight, hairstyle, dress, taste in clothes and cultural epoch are most often the things played with...
Classic Earth 616 May, in her 80s [note: this would be May's age with an adult, late 20s to early 30s Peter].
A taller, more 'Modern,' "middle age to 60s" May
40s-50s May of the Ultimate Spiderman cartoon
Mid 50s May of earth 1811
In ehr early 50s May of Spectacular Spiderman universe (Peter is roughly 16 here)...
The Aunt May from the 1990s Spiderman: The Animated Series. Here, she was implied to be somewhere in her late 60s (being friends with a hero from World War II), but Peter was already an adult in his early 20s in this version. Note her hair is less gray-silver, than light blond, showing she likely had blonde hair as a youth.
Late 40s-50s May of Earth 1610 (again, Peter would be a modern-day teenager)
The 2019 Playstation Spider-man video game version of Aunt May seems to have taken some inspiration from more modern interpretations; here, May is implied to be obviously younger than her traditional "late 60s" portrayal, even though she has a mostly adult nephew. The small stature, friendly face, and shortish hair are more in line with her regular portrayals, but the de-aging and light brown hair make both her true years and ethnicity a little harder to pinpoint.
During the Spider-Geddon storyline, there was an unidentified Earth which had a Hispanic version of May, showcasing that yeah, there is precedence for some ethnic fluidity...but I can't seem to find a picture anywhere, (sorry.)
Of all the visual changes, this "De-aging" seems to be most common in newer interpretations; for some reason, the various Spiderman film series have seemed to have May grow progressively younger than her comic counterpart as they have gone on. This naturally changes her look, varies the age ranges of any actresses who can portray her, and thus makes her ethnicity somewhat fluid, too. This is especially important in relation to the original question; the answer would be specific to iteration of "May" we are speaking of. As shown, there's relative "minor" variation in Aunt May in most comic and cartoons iterations; the movies, however, play by different rules entirely...
Above, we see Rosemary Harris, Sally Field, and Marissa Tomei as Aunt May in the 2002, 2012 and 2017 Spider-man films, respectively.
This de-aging and recasting makes answering this question a bit tenuous; movie media doesn't necessarily have to be in continuity with what's canon, depending on the "take" on the character the director or script calls for. Note how Aunt May in the films moved from the traditional "elderly matron" version of Rosemary Harris (a white-haired English woman in her 70s during the time of filming, who resembled May in face if not body) to a more "middle aged" Sally Field (a 50-something woman with darker Celtic features, who more resembles comic May in size and general personality) to the modern, "hipper", more stylish "yummy-mummy" take Tomei brought to the role, (who flirts, cusses, and where the character's sex appeal was actively commented on in story.)
It should also be noted these are essentially 3 different Spiderman "movie-verses", so while each woman is portraying the same character, it is not the same person at different times in her life.
Specific Conetext answer: So in the Marvel Cinematic Universe, yes, Aunt May is (probably) of Italian descent, insomuch as she's portrayed by an Italian American Actress; it's likely the production team added those touches to the script after Marisa Tomei got the part, not they they were deliberately putting in the heritage element. Peter's "Hot Aunt" is used as a bit of a running gag throughout the films; she is implied to be "too young to be an aunt" while likely being in her 40s to very early 50s, has a more active role in the 15-year old Peter's life, and is even hit on by renowned model-chaser Tony Stark, who also made mention of her beauty.
Some fans of the MCU Spiderman films have pointed out the shared brown hair and similar features as to May's possible closer relation to Peter in this universe, especially the fierce determination she has in keeping him safe after she finds out he is Spider-man. May knowing his identity right off is another "non-canon" change, but what is still kept from the comics, however, is that May and Peter are only related via her marriage to his uncle Ben, ...well, that and the fact that she essentially raised him from the time he was little more than a toddler, so naturally she loves him like her own biological son....
However, it should be noted that in canon and implied in the movies, May spent most of her life in New York... this is important because it was not uncommon for Italian and Irish Catholics to sometimes inter-marry. Parker, as a surname, is more English than Irish, and Peter's religion is (to my knowledge) rarely touched upon, especially in the current films.... but if his Aunt is Italian Catholic, she easily could have married into an English Catholic or Irish Catholic family. So there is a real world valid reason as to why this May Parker is portrayed as an Italian Catholic New Yorker.
