at the same time it's important to use your (nage) hands to protect from any punches the uke might try.
Absolutely! The punches will definitely be next, or at least a grab or something.
Another good move (if you are quick and if you anticipate the fake), is to move to the outside (back) of the roundhouse while blocking the kick in the direction it's already moving in (these blocks are fairly easy - so to speak - as they're not strength against strenght). Then do your stuff, whatever that might be. You'll have your opponent's back in front of you at that point.