Could a successful 20 year old hodgkins chemotherapy recovery cause hypothyroid with a low tsh production?

May be: It would not be practical to link the two conclusively. Hodgkins does affect the immune system and a common cause of hypothyroidism is hashimoto disease, due to autoantibodies to thyroid. The treatment would be the same irrespective the cause.

Maybe: It is theoretically possible, however, hypothyroidism is on the rise due to the endocrine disrupters polluting the environment, and this is just as likely for you.