As an ex Marriott employee I can answer your question.

Technically No you shouldn't get the points (I know it sucks - just telling you the rules) for a no show, or credit for the nights towards your status. Sometimes they do post, but they aren't supposed to.

Faxing the bill to rewards if they don't post probably won't work - the rate code will tell them that it was a billing for a Guaranteed No Show.

I'm shocked though that they charged you ESPECIALLY for ALL of the rooms. We NEVER charged elite members for a no show at my Courtyard. NEVER.