CJT does have limited support on multisite. Meaning it does work on multisite installs, but is limited on control of the Code Blocks on each site within the multisite install. What you said is a great idea to have a Aux setting or even a seperate dashboard for assigning code blocks within a multisite install.
This would be a great development. Unfortunately the senior developer of the CJT project is no longer with us, so I am currently looking for another. I hope to find one soon.