My best guess is no because exogenous testosterone suppresses the natural testosterone production regulated by the body's HPTA (hypothalamus-pituitary-testes-axis) system due to the negative feedback loop caused by too much testosterone and estrogen in a males body. Since this reaction is specific to the presence of excess testosterone, the HPTA is reacting to prevent excess testosterone only.
Someone who knows more about GH and it's effects should probably answer this more fully.