To start I would like to remind, that I do not think pedophilia (by which I mean having sexual thoughts about children) is a sin, but an occasion of the sin of lust. I also believe it can be healed by God's grace.

I think that all sexual relationships with a child will eventually hurt it, because:
1. Even if pure, Godly love grew between an adult and a child, it would eventually end, because the child would grow up.
2. If a child had a sexual relationship with an adult, it would have a VERY BIG secret to keep from its loved ones. It would propably have to lie to keep the secret, which could ruin some of the relationships the child has.
3. If the relationship was ever uncovered (even without proof), the child would face living hell (people convincing it to testify against the adult, mental health professionals etc.).
4. There is a strong possibility that a child would realize the adult's attempt to sexualize the relationship, or assume that sex was the adult's reason to begin the relationship. That would propably leave the child feeling betrayed and hurt and might cause it to reveal the relationship. Even the thought that an adult friend of a child is a pedophile (even a non-offending one) might hurt it.

I would like to stress the fact that many of the above points also apply to asexual relationships.

The main message of the Gospel is to LOVE one another. How could I begin a relationship with an innocent child that I LOVE knowing, that the relationship would hurt it?

Since a close relationship with a child is not an option, that leaves us with the following ways to act on pedophilia:
1. One-time sex between an adult and a child
2. Sexual thoughts about children

I believe that both are sinful and wrong. I can go more in-depth on those if anyone would want me to.

PS. There is a way to "use pedophilia" to help our relationship with God that I am currently using:
Because of our abnormally high interest in children we can more easily relate to one of them. When I see one that is sad, I pray to God to help the child, because I can't. This way I am learning to love others and trying to make their lives easier.