This is actually an interesting idea, but as many have pointed out most outfits are going to have their own medics. In most class-based games the medic is the linchpin that holds everything together; if an outfit is going in without a medic, they've probably already lost.
In addition you're probably going to have a hell of a time clearing your way to the wounded with only medics; take a scenario of a base under siege. Your Auraxis 911 hotline gets called with a bunch of people pinned down, getting lit up. The enemy's got MAXes, infantry, vehicles, and you've got...a group of medics. Might be combat medics, but even so, you're going to have a hell of a time getting where you need to be.
But, definitely good luck if you're looking for something like this. (Or even thinking about organizing it) It'd definitely be something to see. If you're up for becoming a medic attached to a 'standard' outfit with more than one class type, though, check out
www.darkside-empire.com. We could use a good medic.