How to report on sparse areas of sparse fact table
This is a common design pattern for HR systems, so there's any amount of precedent for this type of approach.

You will find that the format used by SSAS stores this type of data quite efficiently, so data volumes won't be a significant problem.  I've seen this done on a HR cube with a row count around 300 million on fairly old hardware using AS2000.  2008R2 on modern hardware shouldn't have a problem with it.