You can use Royal Icing as "glue", but your problems here would be stability and wearability.
Like Becky said, Oreos are round and can only be put together a certain way.
The problems I see with this is that Oreos are not stable enough to handle being "glued" together and being able to be held without breaking the cookie part. I also know from experience, unless you are EXCELLENT at making the right consistency of Royal Icing to hold something like this together, it just wont hold it.
You can try, but I will be shocked and amazed if you pull this off! And if you do, I definitely want to see pics!!!