inlgames.com/weinnachts.htm
The annual WWI Christmas Truce football game does.
In the real event, casualties were evacuated from No Man's Land during the festivities (that included the football game). You get to move your medics around the pitch. If a player kicks the ball into either set of medics, they break the truce and automatically lose. I've never seen this happen, but I have seen tactical deployment of medics to block lines of advance.
Also, the new Christmas themed game will feature them, as they featured prominently in the referent material.
I also aspire a Marie Curie escort game. In WWI, she used her x-ray discoveries to create a portable (in a jeep like van) X-Ray machine to take to the front to aid doctors. She was told that the Army was not supporting transport back and forth to the front. Her reply was along the lines of "So 
what? I don't work for your Army!" You can either help me, arrest me, or ignore me. Your call.
I have a few other medical escort scenarios to leverage for that one.
