Can levothyroxin help a goitered thyroid?

To some extent. If a goiter is due to primary hypothyroidism then levothyroxine allows TSH to come down thereby removing one source of goiter. However, patients with hashimoto's also have lymphocytic infiltration of the gland which contributes to goiter development also. That takes time to go down. We see this in patients with nl thyroid function also. Grave's antibodies stimulate thyroid growth mimicking tsh.