Is there a connection between optic nerve swelling ( papilledema) and thyroid cancer?

Typically no: Typically not, but there could be a problem with the pituitary gland, or a metastatic lesion from the thyroid cancer. Both would be unlikely, but possible.

Minimal: In the unlikely event that unrecognized or undertreated thyroid cancer might spread to the brain and cause optic nerve swelling, then this is an outside possibiliy. Thyroid cancer is slow growing and can usually be managed so that this will not happen.

Papilledema: Papilledema always requires evaluation by an eye md. The causes are myriad including but not limited to inflammatory causes, hypertension, vascular occlusions, ischemic causes, hereditary, compressive causes (tumor), and some medications. Thyroid disease like graves' disease, can compress the eye muscles and optic nerve causing swelling. Thyroid carcinoma can metastise to the eye.