I am going to have a lobectomy in 2 weeks - I have a "suspicious for neoplasm" nodule on my right lobe of my thyroid, so at this point I don't know if it's cancer or not.
From what I have read, there is no evidence that fine needle aspiration spreads cancer. Lack of evidence doesn't mean it doesn't ever happen, but most sites I have looked at say "if it does happen, it is extremely rare".
For my fine needle biopsy, the doctor explained that the needle they use is extremely thin and doesn't pull out that many cells. I guess if my nodule is cancerous then there is a rare chance that the biopsy has spread it, but my main concern at this time is to just get the nodule out and find out if it is an adenoma (benign at this point but could become cancerous if left in), or carcinoma (cancer), and then figure out if it's already spread and go on from there.
My understanding of the current treatment for thyroid cancer is that if you are found to have cancer following a lobectomy (which is a possibility for me), you will need to have your remaining lobe and isthmus removed in a second surgery, as well as tests to determine if the cancer has spread including radioactive iodine uptake test, followed by treatment with radioactive iodine to kill off metastasized cells if it has spread.
I'm not sure if you've had a lobectomy already or if you are in a similar position to me where you may or may not have cancer - if it is not cancerous, I would not worry about the biopsy spreading it. If it is cancer, discuss your concerns with your doctor(s) and hopefully they can help you understand that risks of spread and find the best treatment for you.
Best of luck dealing with this - I've been in waiting for 2 months now since finding out mine was suspicious and I think the worst part for me is the waiting and not knowing!
No experience with it myself, but for your consideration, I wanted to mention reading that only 25% of patients with lobectomy find that their remaining thyroid tissue is able to supply adequate hormone, requiring them to take replacement thyroid med. anyway.