Yes, it is possible. I have cured my hypo T, easier if you catch it before medication IMO.
As Violien, I took enough Iodine to combat it. and co factors.
To reduce the hyper side, I also had some symptoms of it (racing thoughts, palpitations, insomnia); enough magnesium in the right form has helped a lot; but I needed to take it for a long time before I could see the good results.