You cannot say that someone's well being is directly affected by attachments but you can say that they are related. Other things such as the environment the child grows in affect his/her personality. An attachment does in fact influence this though because a child can gain encouragement from that attachment. For example a parent could be an attachment and these parents could encourage their child's or inspire their child to succeed. This influences and does indeed inspire the child but it does not determine their success.
I agree with the idea that the environment in which a child grows up can affect their personality and therefore both their attachment and well-being. All of these elements would be related, but would not necessarily determine the future of the child.
