TLDR: I don't know how large is "very large" but probably yes on all counts. But a smaller breed with course, dark hair was more common throughout Rome.
The Ancient Romans understood some basic mechanics of selective breeding. They might not have been breeding desirable traits so that 100 generations in the future you’d have a better breed. But they understood that breeding a large sow with a large boar would tend to produce large offspring. When selecting breeding stock:
According to Columella (7.9.1), boars should be of great size, with huge haunches, but not correspondingly long legs and hooves. Palladius (3.31) adds that they should be great-bodied, ample and round, with large hips and white bellies.
Sows, on the other hand, should be large-bodied and pendent (Pallad. 3.152), but also long in shape (Col. 7.9.2).
Did any Ancient Roman pigs have the same general look of what we’d recognize as a contemporary domestic or wild pig? Yes, definitely. Here’s a cast of a pig found in the Villa Regina, Boscoreale, near Pompeii. https://www.flickr.com/photos/70125105@N06/13896292832
Looks like it was alive yesterday, not almost 2000 years ago.
There were at least two common breeds of pig. The dominant one
was similar in appearance to the wild boar, with hard, dense, black bristles (Col. 7.9.2; Pallad. 3.152; Lucr. 5.969-970).
These pigs were likely herded (or hunted) in forests and made up the majority of pork throughout the land.
But a larger breed was also described.
Smooth pigs and even white ones (Petron. Sat. 47; Juv. 13.1 17-1 18), however, may also be pastured in warmer and sunnier regions (Col. 7.9.2).
(Note that today all light colored pigs are called “white” and dark pigs are called “black.” I think that's the way the term is being used here.)
This larger breed was somewhat associated with millers and was likely kept in sties closer to (or in) cities. They cost more to produce and were probably the breed more often used in religious ceremonies / sacrifices.
Of pigs depicted in art, MacKinnon lists some extant examples. Among them is this pinkish-brown pig from the Villa of Mysteries: http://www.gettyimages.com/detail/illustration/fresco-from-villa-of-mysteries-pompeii-campania-roman-stock-graphic/148355051
Size. MacKinnon has stats on pig size from analysis of bones. It's too hard to estimate length. Height (withers) is in the range of 57-85 cm, with pigs found at Settefinestre in a complex of 27 sties falling mostly in the range of 75-80 cm. So these pigs raised for the market were large but not "very large" by today's standards. Pigs found in cities tended to be slightly larger than rural findings.
Michael MacKinnon. High on the Hog: Linking Zooarchaeological, Literary, and Artistic Data for Pig Breeds in Roman Italy. American Journal of Archaeology. 2001. pdf with free account.