Is it possible to get a good alignment reading if the control arms were out on backwards ?
Yes it is possible, but depending on which ones you are talking about, you will not be able to turn your front wheels very far before they hit… If the distance from point a to point b is the same weather the part is one the wrong side or not then, it will not effect the alignment… but again, you will have interference issues front or rear with turning the front wheels, or the inner wheels rubbing the part, or suspension travel/binding front or rear…
I had a tech install Honda outer tie rod ends on the wrong side and align it up perfectly, but the wheels would not turn left/right very far, I pulled the vehicle back in and swapped sides and pulled it back up on the alignment rack and it was in specs… Yes I called him an idiot afterwards…