your best bet would be to start your gh and after 2 months go in to the Dr and have your thyroid hormones tested. i've heard that it is possible for gh to effect your t4 levels, but personally, i have never came back lower than normal, while using gh. ideally, i would not want to run any thyroid drugs while in the off season. some say that they like to to help keep leaner and maybe up regulate protein absorption some, but if you don't need it, i feel it would be better off not to mess with your hormones and possibly cause a greater issue down the road. if you feel you want to be a little leaner in the off season, adjust the diet a little. 

a concern that i do have with gh is that it can make you insulin resistant. this will make it harder to utilize the food you eat. thats why bodybuilders often combine gh with insulin. that is a whole other topic.