"In chemistry, molar concentration, also called molarity, is a measure of the concentration of a solute in a solution, or of any molecular, ionic, or atomic species in a given volume."
Generally speaking I can't see a reason why you can't use molarity this way, although you will be in troubles - because it is usually not used that way. First you will have to convince everybody around to use such units. But technically they seem to be OK, unless I am missing something.
Question is, whether you will find practical application, creating units for units sake doesn't make sense.