Supposedly now you can even hook up laptops or other devices now to send large encrypted messges over the ham airwaves, which could include encrypted voice comms. Add into that the coded words you mentioned and it could be more than trivial for anyone including NSA to acquire and decifer.
It is illegal to hide messages in ham frequencies by the use of encryption. There may be some loopholes for incidental encryption used for authentication or other purposes. But as other commenters point out, there is no way to detect encryption that is inserted into plaintext cover messages. For example each particular spoken word could be selected to encode a bit or two of encrypted data. The spoken words might sound a bit strange but can’t be proven to be cover for encrypted messages.