Does rai normally eradicate the cancer cells in metastatic sites of papillary thyroid carcinoma? Or does it only reduce the tumors in these sites?

Eradicate. Rai can eradicate thyroid cancer cells from distant sites such as the lung or bone. It may not be completely effective with everyone, however, as some tumor cells at these distant sites have lost the ability to take up the iodine like normal thyroid cells can. In such cases, repeat and/or higher doses may be required.
By definition.. Tumors in these metastatic sites are the papillary cancer that spread and rai usually destroys them!