Yup, information theory says that Gaussian signalling is optimal in term of bandwidth utilization in many cases. And we've spent decades trying to achieve this

Yup, information theory says that Gaussian signalling is optimal in term of bandwidth utilization in many cases. And we've spent decades trying to achieve this by various techniques in coding and modulation. And yes encryption/secrecy adds another layer of randomization. I believe a radio signal eavesdropped from a US military base is not much different than some random noise. That being said, the question is to tell if a signal is man-made or not, which is much easier than to discover what information it conveys. Based on modulation carrier frequency and the transmit (on/off) pattern you can still very much tell if that signal is man-made or not.