Big Foot said:
The Bravery Medal is not only a cadet medal, to the best of my knowledge all Canadian citizens are eligible to win it, should the circumstances warrant its awarding. It can be awarded to civilians and military personnel. It does not warrant the use of post nominal letters.
Actually, the postnominals for the Medal of Bravery are "M.B.".
Canadian Orders, Decorations and Medals - Precedence: Honours This site shows the relevant, and correct, postnominals for all Canadian Orders, Decorations and Medals. Some people might want to take a look at the postnominals for the Canadian Forces Decoration, notice you don't see "C.D.1/2/3"... :

You may be surprised at the number with postnominals as all Orders and Decorations have them, as well as 3 of the Medals.
As for Cadet Medals qualifying for postnominals, you should probably note that the RCMP Long Service Medal, the Police/Fire/Corrections/Coast Guard/Emergency Medical Services/Peace Officer Exemplary Service Medals, Ontario Medal for Police Bravery, Ontario Medal for Firefighters Bravery etc don't have postnominals either, and these are medals "officially awarded under the authority of the Crown" and take more than "...successfully complet(ing) five years of honourable service with no serious infractions,and be recommended by the Cadet Corps Commanding Officer." to be awarded. I held out a bit of hope for your idea when I saw the Ontario Medal for Good Citizenship had the postnominals of O.M.C. but once I saw that the Commissionaire Long Service Medal didn't have them, that faint hope was dashed.
On the other hand, perusing your link I see that I'm eligable for the Army Cadet Long Service Medal:
6. All Army Cadets past or future shall be eligible for this award.
Guess I'll have to fill out the form, send in my $10 and sign whatever petition you're going to get going for this whole postnominals hooha, as I think it'd be quite neat to have Mr Meat Head C.D. A.C.S.M. on my cheques...
Interestingly enough it appears that there has been, or may be, an attempt to get this medal officially recognized:
11. ... The Army Cadet Service Medal will be worn at the extreme left of all decorations and medals of the Cadet system, all in accordance with existing dress regulations of the Canadian Cadet Organization and, if/where permitted, of the Canadian Honours System.
Be interesting to see how many guys actually applied for the medal and had it mounted if that happened.