Sorry, I didn't really think through the situation. Of course the update wouldn't force the drawings to rebuild from the model.
But you can use the "Rebuild all Drawing Sections" command followed by the drawing update. If you can't find this in your Work Environment you may need to add it. I suppose the drawings could also be set to update automatically to speed this up a bit. (I tend not to use the auto update to avoid unexpected and potentially embarrassing prints of work in progress.)
Of course if you don't want to rebuild all of them it's pretty quick to right click on the section name in the project map. This only works one by one but is pretty quick if the sections don't take to long to rebuild.