As Minnie Mum said, the answer is generally no. There are always exceptions to every rule and someone is bound to say that they've been able to get <fill in the food> from <fill the restaurant> to go. It really depends on the restaurant and how busy they are. None of the Disney venues are set-up to handle straight take out orders, so the best you can do is ask, but be prepared to be told no.
Alternatively, you can make an ADR, be seated and then when you order your food, ask for it be boxed. I know the the restaurants have doggie bags for left overs, but you'll an ADR and to be seated. (Though I've never tried to take soup as a left over, so I don't know for sure they have soup containers - I just know they have boxes to pack up leftovers and desserts.)