If you have a custom tune, you can usually leave it as-is unless the rear o2 sensors are turned off, and that's only in places that do OBDII testing. It's not just a matter of codes, it's a matter of what "monitor tests' are "not ready"; typically you can only have 1 or 2 not readys, and if you have more, you will fail (IF they do the OBDII test). Turning off rear cats results in 3 not readys (as I found out the hard way one time!).
If they just do visual, you can run your setup as-is.
If you can run your stock tune with your cai (or with an appropriate insert), then that would be the safest way to go, if you are uncertain.
Most of us with custom tunes use them and pass inspection with them, even in OBDII testing areas.
Good luck!