You are best off consulting a basic physiology textbook (Sherwood is easy) for:
(1) GH regulation
(2) In the grand scheme of things, will the effect upon GH secretion be significant to your goals.
As a starting point…
Table 3ï¿½??3. Factors that Regulate Growth Hormone Release
Stimulation of GH release Inhibition of GH release
Excitatory amino acids FFA
GHRH = growth hormoneï¿½??releasing hormone; IGF-I = insulin-like growth factor-I; FFA = free fatty acids.
So does insulin directly inhibit GH release? It would seem not to. But somatostatin is released in response to the same things that cause insulin release (ie. a sugary meal). So a sugary meal would cause somatostatin release, and thus inhibit GH release whilst insulin is also being secreted.
But then, are there excitatory amino acids in your protein drink (I have no idea which amino acids are excitatory in the context of GH release, I’d have to check)?
It’s a massive interplay of factors, and I don’t know enough about the product, or endocrine physiology in general to give you an answer.
Maybe someone else knows more about it and can answer you, but I doubt it really, because at the end of the day, the effect on GH will be insignificant to your overall progress.