Stephen

Short answer: NO
Longer more verbose answer: The majority of people do NOT lose their teeth from radiation TX. As Christine notes, the deciding factor is the condition your teeth were in before radiation. Often patients have their teeth taken out before the radiation to avoid problems that are foreseeable.
My doctors insisted I see a specific prosthodontist (a dentist with advanced degrees) who specialized in oral cancer patients for a complete evaluation before TX. He cleared me for TX but noted I would need work afterwards. Basically once you have radiation, it's problematic to have any teeth pulled since the jaw may not heal. Getting cavities filled, crowns put on, or even root canals are all okay (I've had all of that done after my first bout of radiation with zero problems).
I do use my flouride trays every day even though I don't eat since the mucous actually supports plaque & decay.
Get recommendations from your treatment team on a dentist or prosthodontist as cancer doctors usually know good ones with cancer experience.
Charm