IDK... I feel like saying no would be a lie because I'm sure I'd get curious. As much as you want to give your children freedom, there will come times when you have to step in and intervene with what they're doing. You could have raised your child to be the best child on Earth, but all it will take is one manipulative person on the Internet to change everything. If I did go through their history, I wouldn't take it too far, just enough to see if anything is suspicious and to see if I need to have a talk with them.
Parenting is tricky so it's hard to say a definitive yes or no.