Unless they are looking for them, they are easy to miss during a PAP test because the speculum is in the way. You should ask if you are worried about internal warts. They also don't always show up right away.
As for your specific question about having warts that are not sexually transmitted. Depends on the wart. There are over a hundred different strains and they like to reside on different places on your body. e.g. some can only live on the skin of the palms or soles of the feet, some can only live in the genital area (hence 'genital warts'). You don't need to have intercourse to get genital warts, but very close contact with someone who has them.