Absolutely it will. Thyroid cause the inflammation of the noids in the throat so naturally it will cause a lump and stop the natural flow in the throat.
If your thyroid is overactive you can develope what is called a goiter. These are very serious and you must see your doctor immediatly as they can cause you breathing problems if not treated.
Thyroid problems can cause throat pain when the tyroid is enlarged. Ususally medicine or surgery is the best solutions for this problem. Lifelong medication will help regulate the thyroid to the numbers it is suppose to be.