Yes, I do believe a colony of domestic rats, if let loose, can become feral and reproduce and live just fine in the wild. But I think it's weird rats are illegal as they are native to almost every nook and cranny of the world. It's not like someone let pet rats loose they would be introducing a non-native species.
While there are species of rats that are found around the world, the pet rat (
Rattus norvegicus, the brown rat) is an introduced species. The other rat that is commonly found running around is the black rat,
Rattus rattus. Among other things, the whole stowaway-on-a-sailing-ship thing is true... and at least partly how the rat became so widely spread around the Old world (and probably the New).
And just because I can, since it's easier to list what's *legal* in CA than what's not, I'm just going to add CA to the list. [off the top of my head - legal: livestock. Dogs, cats. Domestic rabbits, rats, mice, guinea pigs, hamsters, chinchillas. Many reptiles and fish. Most psittacines (parrots), many non-native songbirds.]
Bears- Pennsylvania, CA
Big Cats (lion, tiger, liger, cougar, etc.)- Pennsylvania, CA
Coatimundi- California,
Crocodilians (alligator, caiman, etc.)- California,
Degu- Pennsylvania (illegal to import and no licensed breeders in state), Douglas County NE,, CA
Ferrets - California, NYC, CA
Fox- Pennsylvania (red and grey, unsure of Fenec), CA
Flying Squirrels - Connecticut, CA
Hedgehogs - Arizona, California, Pennsylvania, Douglas County NE,
Monkies/Primates- California, Colorado, Connecticut, Georgia, Kentucky, Louisiana, Maine, Maryland, Massachusetts, Minnesota, New Hampshire, New Jersey, New Mexico, New York, Pennsylvania, Rhode Island, Utah, Vermont, Wyoming
North American Opossums- Pennsylvania, CA
Pitbulls- Denver, CO; illegal in Miami Dade county (FL); Columbus, OH;
Prairie Dogs- California,
Quaker Parrots- California, Pennsylvania (thanks for the tidbit from my MiL)
Raccoons- Pennsylvania, CA
Rattlesnakes- Pennsylvania, CA
Skunks- AL, AK, AR, AZ, CA, CO, CN, DE, GA, HA, ID, IL, KA, KY, LA, ME, MD, MA, MI, MO, MN, NB, NV, NC, ND, OK, RI, SC (after current captive animals have died), TN, TX, UT, VT, VA, WA, WV.
Serval cat- Pennsylvania, CA
Snapping turtles- California,
Sugar gliders- Massachusetts, illegal in Minneapolis/St.Paul (MN); Pennsylvania; CA
Wolves- Pennsylvania (hybrids are accepted, I think), CA
Wolf/Dog hybrids- California