If you have a court appointed attorney and they add a private investigator to the team, is the investigator allowed to communicate with the ADA/DA about plea deals?
No, the private investigator is not allowed to communicate with the ADA/DA about plea deals or anything else EXCEPT as specifically authorized to do so by the defense attorney,. The PI is working for the lawyer; he is part of the legal team and all communications from the prosecutor's office must go through the lawyer. That means either that the lawyer him/herself communicates or, since an attorney can have people working with or for him/her make contacts on his/her behalf, the lawyer must specifically ask one of his team to communicate and authorize them to so. In all events, who communicates is under the lawyer's control: the PI cannot talk to the ADA/DA without the lawyer's knowledge and instructions to do so.