After my complete thyroidectomy, I was off Synthroid for 7 weeks before doing the RAI treatments and it was the worst 7 weeks but it didn't affect my menstrual cycle.
I assume they are planning I-131 for thyroid cancer??
You may want to review the pathology with your doctor, confirm need/dose for I-131 and discuss possible thyrogen use so you don't need to be off medication (which we usually do for 3 weeks prior to I-131 if withdrawal from meds needed). But to answer your question....it will effect flow and duration of cycles.
Umm that is quite strange that ur doc isn't at least starting u on a low dose of thyroid med right away. I got my thyroid taken out 3 yrs ago and got started on a low dose and even with that had a hard time just walking to the bathroom bc of the lack of energy. I had to go up 4 dosages to get to the desired level. Good luck to u, just make sure all the instructions and advise from ur doc is best for u