Are thyroid nodules more or less likely to be cancerous when one has been taking synthroid (thyroxine) for 20 years?

Depends: If autoimmune thyroiditis is the reason you are hypothyroid, then there is about a 3 fold increase in risk for developing thyroid cancer over those who don't have anti thyroid antibodies. Having said that, thyroid cancer is still relatively uncommon despite a growing incidence.

Nodules: No correlation with synthroid (thyroxine) use. Nodule changing to malignancy correlates with age of patient and size of nodule. Older patient more likely to have cancer.

No effect: The act of taking synthroid (thyroxine) has nothing to do with the potential for thyroid nodules to be cancerous. Radiation exposure, smoking, family history of thyroid cancer elevate the risk for a nodule to be cancerous. The nodules are typically followed by ultrasound over time. If one or more significantly changed in size, biopsy is needed.