Hi Dithers, I would hate to dampen your enthusiasm and would not say that would you going to achieve is pointless, cos all training is good! But.........
Where CRM really matters in the 2 crew environment you would almost certainly need to complete an Operators CRM package during your initial training. This is because part of the package includes the Company SOPs, Checklist philosophies etc which need to be given during the Operator's Conversion course in any event and the CRM vehicle just makes this convienient.
I could not really see your CV being considered above another because you have a CRM course completed.
Just an opinion which I hope will help you.
DB