Goiter. Yes -- it can and often does. Goiter is usually an inflammatory reaction caused by an autoimmune disorder. This can wax and wane as antibody levels do. Sometimes thyroid hormone replacement can shrink it to a degree but not always.
Sometimes. If the goiter is due to low thyroid hormone levels, taking thyroid hormone tablets may allow the goiter to shrink, but does not always. If the goiter is due to a condition causing it to make too much thyroid hormone, then treating that condition with medications or radioactive iodine-131 might also shrink it.