No. Having sex with children is illegal in all 50 states. As is viewing child pornography. That is not the same as being a paedophile. You cannot be tried for a crime you haven't committed.
Let me explain it this way.... Punching people is assault and you'll be arrested. Thinking about punching people is not a crime, you can think about punching people all you want. You can even think about murdering people all you want - you just can't DO it.
Unless you have some sort of mystical way of looking into people's thoughts, you have no idea whether someone is a paedophile or not. You have to wait for them to DO something, then you arrest them and throw them in jail.
Paedophilia is the motivation. Statuatory rape or sexual assault of a child or distribution of child pornography is usually the crime. The distinction is important.