I haven’t actually configured G-Suite Relay for email but it seems as if you need forum.neuronootropic.org to be added and verified as a sending domain in your G-Suite admin account. if that’s the case, given the google documentation, there is no reason for it no not work.
However, if you have neuronootr0pic.org verified at G-Suite you could use something like noreply_forum@neuronootropic.org to send email.