It's more but still not that much more considering the exponentially added cost to recruitment due the the law of diminishing returns if there were no women in the military.
Unsurprisingly the facts say otherwise. The Army takes in almost three times as many recruits as do the Marines (20.5 % to 6.9% according to http://www.defenselink.mil/prhome/poprep2001/chapter2/c2_raceth.htm) But the Army spends "more than $11,000 for every new soldier this year, more than any other service ever." The Marines: "The Marine Corps spent the least per recruit, $6,006" (source http://armedforcescareers.com/articles/article12.html).
According to your theory the Army should be spending a lot less per recruit than the Marines, instead they spend almost twice as much. Of course this might be because-according to http://www.dod.mil/prhome/poprep2001/chapter2/c2_gender.htm-"The former annual DoD-sponsored Youth Attitude Tracking Study indicated that young women, depending upon age, were approximately one-half less inclined to join the military than young men". Therefor they require more convincing to join (another way of putting that is that it costs more to recruit them).
Of course your argument only holds water if females are less expensive than males overall even if they save money on recruiting. But wait-according to the same link I just gave a minute ago-http://armedforcescareers.com/articles/article12.html-"The Pentagon spent $1.8 billion on recruiting this year, less than 1% of its total budget." I've already shown that females are more likely to be injured than males, and more likely to use hospitalization. Total military health care costs-per http://www.policyalmanac.org/world/defense_spending.shtml-$14.8 Billion.
So much for your theories.