I posed this question to the Director of College Relations at my institution, whose office is responsible for recruitment.  What follows is his response:
I am not aware of any studies that have
been conducted regarding recruiting costs.

You might contact the American Association of
Collegiate Registrars and Admissions Officers.

The American Council on Higher Education just recently completed a
comprehensive study on the cost of higher education in general and AACC has
some of that data available.

CASE, the Council for the Advancement of Science and
Education,  may have done studies or  published  literature on this

All these groups have websites.

In our professional group, some of our members have done some informal
surveys about how much colleges budget for the marketing and PR function.
But the information is generally used internally by the person collecting
the data and is not shared.

Part of the problem with available data and studies in this area is the
question: What constitutes the cost of recruiting a student?  No one to my
knowledge has developed a standard definition of this aspect of cost that
is generally accepted by all.

I hope this is helpful.

Gail Platt