I have to say I dislike this idea.
There are already enough stalemates in this game. Medics would exacerbate the problem. Adding a class that can heal or worse, revive would imo take away from the enjoyment of the game, making the standoffs ever more prevalent. The game already has several ways of mitigating damage (abilities, cover, armor, inserts, etc) - so adding a class that does nothing but duplicate (and expand upon) those features, is well.. redundant.
Now, if the maps were reworked to be more open and less linear, then I could maybe see a point (less standoffs) - but even so, I think it would completely change the way the game is played, and worse, would change the gameplay in a negative fashion.