This question was raised on a blog I read, and recommend to anyone with an interest in adoption. http://diaryofanadoption.blogspot.com/
I personally do not like the word 'normal' any more than 'abnormal' as a word to describe a human being or their life experiences. I prefer usual, as this is, in my opinion, what people mean when they use the word normal and I feel it is a much less loaded word.
So in terms of usual where does that leave adoptive families? Yes, adoption is an unusual situation, yes adoptive families are different, and yes, adoptive children will all have problems of varying severity related to the separation from their birth parent/s and their early life history.
However we are also families who adapt our parenting to suit our individual children, who see our children as the individual child they are and not just a label so that society can put them (and us) in a convenient box.
Those who discuss the 'normality' of adopted children or adoptive families, IMO are likely to be fishing for Daily Mail type information on our kids early history, and I for one do not share those details of my child's life with these people. It is his history, and as far as I am concerned it is his sense of what is normal which holds greatest importance to me.
Thanks be to God for my unusual family!