USAF gets to "play" as well.
Interestingly enough, when former SECDEF Dick Cheney's drawdown was implemented, it did not, for the most part, apply (in equivalent measure, anyway) to medical personnel. This posed a real challenge for installation commanders, because due to specialty constraints within the Medical Service Corps, and what is known as "stovepiping" (concurrent chains of command and head butting at the flag/general level), these assets were almost "on ice" and could not be diverted to other collateral tasks to take some of the workload when other support staff were cut. As a consequence, you had support staff working their asses off, and medical personnel doing light duty at some installations. Boy, has that changed! The medical staffs are stressed and overstressed right now.
Makes you ask this question: was this whole drawdown charade a long-range plan?
Anyway, CG medical assets in Iraq are negligible. They do play a big role in the deployment readiness equation, of course. If you want to see their lessons learned slideshow, you can find it here (PDF, need adobe to view):
http://www.usafp.org/Word_PDF_Files/Syllabus-2004-Annual-Meeting/Tuesday%2023/03.5Tedesco%20OIF.pdf