It seems unlikely. There are plenty of diseases transmitted via contact with pigs or by eating pork - anthrax, brucellosis, leptospirosis, tetanus, staph/strep infections, etc. But all these diseases can be just as easily transmitted by other animals, including cattle, sheep and goats, rats, wild game. In fact in most cases, pigs aren't even the most significant reservoir, some other animal is.

One disease specifically caused by pigs is the pork tape worm, Taenia solium. It's transmitted through eating under-cooked pork. Usually the worm resides in the human gut and can co-exist for decades without producing any debilitating symptoms. But occasionally the eggs pass through the intestinal wall and become lodged in other tissues where they cause cysticercosis. They can cause serious symptoms including epilepsy if lodged in the brain, or even death.

Humans have known about these worms since pre-history. All intestinal worms are frequently passed out in the feces, and any worm large enough to be easily visible to the human eye would have drawn attention. This would have included the tape worms - solium, saginata, asiatica, as well as round worms or other big worms.

However, we didn't know how we acquired these worms until quite recently, so it's hard to make a case that humans avoided pork to avoid the infection. Edward Tyson was the first to scientifically describe tape worms in the late 17th century, but even then they didn't realize that there were two major species - saginata, the beef tape worm, and solium, the pork tape worm. It wasn't until the middle 19th century that Kuchenmeister first described how to differentiate the two based on differences in the scolex, or head of the worm.

Similarly, we didn't know the role pigs play in their transmission until Johann Goeze first observed in 1782 that the heads of the tape worms resemble cysts sometimes found in the muscles of pigs. And again, it was Kuchenmeister in the mid 1800's who made the causal connection by feeding cysts from pigs to condemned criminals (!) and then observing worms in their intestines after the criminals were executed. Medical ethics was lax in those days. A couple decades later, J.H. Oliver made the same connection for the beef tape worm - Taenia saginata - by observing tape worms in the intestines of people who ate "measly" beef. This was 1869.

So it's hard to argue that the ancient Hebrews avoided pork because of tape worms when in fact the connection between pigs and tape worms was discovered less than a couple hundred years ago.

Another way to look at it is to observe pork eating populations in the days before it became routine practice to screen pork for cysts. I am not aware of any studies indicating that such populations have higher morbidity or mortality than populations that didn't eat pork. It would take some serious statistics to discern the net effect, whether the extra burden of cysticercosis is offset by the benefits of eating pork (since pigs have the best feed conversion ratio among domestic mammals, and will turn inedible scraps into pork with high efficiency). I doubt any such study exists.

It seems that the common explanation - that pigs have "dirty" habits - is probably more likely as the reason for the religious ban. Pigs eat pretty much anything, including human feces. This may be why they were considered offensive. But it's just speculation, we don't really know.