Could rhodiola cause low TSH levels?

Unlikely but... Rhodiola is known to improve thyroid function and thus might be expected to reduce TSH levels somewhat (though more research on this is needed). However, a low TSH tends to be a sign of hyperthyroidism and, as far as i know, rhodiola is not known to stimulate the thyroid to the point of hyperthyroidism.
Very unlikely. There is no known effect of rhodiola on the hypothalamus, pituitary or thyroid gland. Low TSH is almost always associated with hyperthyroidism or a pituitary problem. See an endocrinologist for evaluation.