The vet may be right about waiting and seeing as long as he is able to breath and is still passing feces. Although, I don't think it is true that he could have not been x-rayed. I am not sure but I think is more that he or she doesn't think it is necessary based on the information you gave him. There is a soft tissue technique used in radiography. Conventional plain films, especially lateral techniques of the larynx that provide preliminary or definitive information about foreign bodies, trauma, and other types of acute and chronic airway obstruction. These radiographs can demonstrate soft-tissue swelling, alterations of the cartilaginous framework (if sufficiently calcified), and the position of the air column. This is done by lowering the kVp thus the pentration of the usable x-ray beam. Now, you can still see plastic in an x-ray depending on its size. I have seen something as small as a asprin in a radiograph before.
Sorry, I just don't like for people to be given the wrong information....I feel that instead of telling the patient it can't be done ....and assume he or she doesn't know better....they should tell the truth and say that it is not necessary because of ect. ect.....and ect. I would assume the vet knew that it would be possible if he felt it was necessary. Sorry, for my soap box..