Executive privilege aside, of course not. I assume by civilian authorities you mean political appointees. There are instances where career DOD civilians supervise military personnel.
If political appointees must be concerned that military commanders will release to the public sensitive, "insider" information against them to challenge their policies and to attempt to remove them from their jobs, then this will certainly have a chilling effect on their interactions. It also challenges the civilian control over the military. The level of candidness will be affected and policy suffers as a result. Also, political appointees may select those for jobs whose political leanings are more like theirs rather than the best person for the job. Personal loyalty becomes more important than competence.
I can't recall very many instances recently where retired DOD political appointees used "insider" information against military commanders in public and called for their resignation or firing. Do you?
...this will certainly have a chilling effect on their interactions. It also challenges the civilian control over the military. The level of candidness will be affected and policy suffers as a result. Also, political appointees may select those for jobs whose political leanings are more like theirs rather than the best person for the job. Personal loyalty becomes more important than competence.
Let me add to that: How does a civilian decision maker know whether a military commander's "advice" is genuine? He now has to factor in the possibility that the commander is simply throwing it out so he can say "I warned them" later. This undermines the civilian authorities' ability to rely on the input of the military.