Thanks for the confirmation. There are occasionally exceptions to general rules and practices, so I was not absolutely certain. Reality does not always follow common sense.
I cannot think of a single case where we put our people into civilian ATC environments. I cannot think of any need or justification.
CF aircraft departing from/arriving at/flying over what is primarily a civilian airport have no need that cannot be satisfied by civil ATC.
There are most likely AC Ops in 1 CAD HQ, but they would be in staff positions and therefore a bit more senior.