Going from the court decisions, they would know that traffic is illegal if a court tells them it's illegal. Again, refer to People v. Brophy: the common carrier is not "authorized or required" to investigate. Probably meaning they can aid in investigation (e.g., supply information to police) but not perform an investigation (analyze said information themselves).
In addition, Title II would probably put internet traffic on the same level as wiretaps in terms of (non-DHS) data snooping. If anything, it would give internet users more protection for this sort of thing than they are granted now.