This is very early for a PET, and makes me wonder what the doctors are thinking.
Make sure that they are prepared for the area of treatment to really light up, it is no doubt still in repair mode and the inflammation there is going to make the scan worthless in that area. However, if there was suspicion on the doctors part that there was an opportunity to this to have metastasized to a more remote area than the neck, then a PET which looks at everything from the top of your head to your groin would show activity in any other vital organ. Of course that begs the question; if you thought that this might be a possibility why didn't you check this out before beginning treatment? The treatment might have needed to be more definitive and involve different therapeutic agents and techniques to deal with the mets in addition to the primary.
Even in those more remote anatomical places, benign things other than cancer will cause a PET to light up the area, so residual issues related to chemo, as the liver and kidneys are still processing it etc. all could be collateral to his treatments and not disease. Even an infection in the patient's lungs will give you a false positive. So while I'm a big believer that PETs are highly useful, at this stage of the game you have to wonder - with what everyone knows about early PETs and false positives, why are they doing this.