I followed your drift as well as the questions that were asked on Tuesday. Categorically, there are members of the Canadian Forces who receive EI as well as members of the RCMP. My wife was a member of the Canadian Forces. She went on two maternity leaves while she was a member of the Canadian Forces. She received EI while she was on maternity leave as a member of the Canadian Forces. So yes, they do.
The issue is my receiving an annuity from the Canadian Forces. I'll never receive EI.