Is positive discrimination in faculty hiring really efficient at promoting diversity in an academic department?
The effects of affirmative action in academia and corporate environments is a matter that has been the subject of an immense amount of study and scholarly literature, so any detailed answer to this question is probably going to involve some engagement with that literature.  Nevertheless, at the outset, there are some aspects of your question that could be unpacked and clarified, so that you can focus your analysis more effectively on what exactly is of interest:


Define what you mean by "diversity": I suspect you are referring to the promotion of outcomes where the racial composition of the faculty is closer to the racial composition of the host society (e.g., increasing the proportion of people from "underrepresented" groups and decreasing the proportion of people from "overrepresented" groups).  Or do you mean something else?  Either way, you should take a moment to consider exactly what "diversity" would entail, so that you have some basis for assessing efficiency in its promotion.
Consider what you mean by "efficiency": What constitutes "efficiency" here?  Is it the speed with which a particular outcome is achieved?  The cost?  Some combination?  If it includes some consideration of cost, then what counts as a cost?  Does "efficiency" require the academic system to remain functionally efficient, or do you simply mean that the method used to promote diversity must itself be efficient?
Some results follow virtually by definition: If "diversity" is defined as above, then positive discrimination in favour of "underrepresented" groups is likely to increase diversity (at least in the short term) virtually by definition.  If efficiency refers to rapidness and simplicity of the processes then the simplest and most overt forms of positive discrimination are likely to be the most efficient, again virtually by definition.  In such a case, the consequences are so obvious that it is unclear why you would need empirical evidence at all.
Are you even asking the right question? If the sole goal of interest in your question is to be "efficient" at achieving "diversity" then clearly the most efficient way to achieve this is simply to impose immediate quotas in faculty composition without regard to any other considerations.  It could even be achieved simply by appointing all academic positions via random lottery among the entire population.  In other words, your question is rendered trivial.  This happens because you have not posed any trade-off with other considerations in your question.  Does the actual merit of candidates matter?  Does the quality of academic work matter?  Does fairness matter?  If so, then you now have a trade-off between multiple things, and you will have to adjust your question accordingly.