The only way to go about this without code is to reference the template parameter directly in the cube view (rather than going through a Parameter), which works fine if you embed Cube View Components directly. Obviously this does not give you a report, but the CV can export as Report - it's just an extra click.
If you try to go through Data Adapters, this strategy breaks. It is doable via a full Dynamic Dashboard Service implementation (i.e. in code), although in 8.5-9.1 this too is not possible because of a known issue which should be fixed in 9.2.
A workaround (again in code) could be to implement your own DataSet rule that uses FdxExecuteCubeView and returns the same table that a Cube View adapter would return; you then create a Data Adapter of type Method/Business Rule to execute the rule, passing as argument a template parameter (e.g. {MyBR}{MyFunction}{Entity=~!myTplParamEntity!~} ). This should work, although I've not tested it...