This question had been googled and was on my stat counter last week.
I'm not a professional but my mom answer is no. RAD has to be treated. There are varying degrees of attachment. If your child does not have full blown RAD you may see the symptoms of a weak attachment fade as they grow due to your hard work as a parent. It takes specific work on the part of a parent. This doesn't mean just "love them more". That you are not parenting good enough. It means these kids need to be parented a little differently.
I would begin attachment style parenting with a snuggle time each day. This is a time of snuggling on the couch. If your child will do it I would hold them on your lap. You can tell jokes, share stories, and you need to end with you telling them how much you love them. Human touch is very important during this time. If you can, wear a tank top or something so their cheek can be against your arm. This was very effective with Taz and he really snuggled against my arm. Then you feed them caramels or vanilla ice cream from your hand to their mouth. This activity to me is one of the most important things to do in the beginning. When my boys became too big I had them lay on the couch. I sat on the side of the couch and draped an arm across them. Eye to eye contact is important during this time.
At night I would rock them and wrap them in a soft fuzzy blanket. Before you become alarmed after looking at our photo, they were 3, 6 and 6 at the time. We would play a game where I would sing a short song. Eye contact was very hard for them in the beginning. I'd sing a non threatening song like "Row row row your boat". We would play a game where I'd see if they could keep eye contact while I sang the first phrase. If they could it was met with high fives. If not, I'd laugh and say "Oh...too bad. Try again." I gradually added lines until I was singing the whole song. Then I went for the big stuff and begin singing love songs or lullabies.
These two activities are a great place to start.
If you are starting out, read everything you can. Treatment for RAD has changed greatly in the last few years. Read judiciously and glean from each book what you think you can use and would work for your family. Generally the more loving the approach the more likely it is too work, in my opinion.
Give importance to spiritual development. Teach your children to pray. Take them to church. I believe learning that God loves them and that there are real spiritual reasons for right and wrong are important. I'm not telling you what church attend, but please go.
If your child does have full blown RAD, if you are not sure, or just plain need some help please find an Attachment therapist. There is a listing to the right of therapists for each state. You may say you have tried many therapists and they are a waste of time. We tried 8 therapists before finding an attachment therapist. This is different. Just talk to one over the phone and get a feel for if he/she is right for you. RAD can not be out grown but it can be healed.
Never, never, never quit.