From personal experience, yes I believe so. Whenever my medic (with high surgery lvl) gets knocked out, everyone starts dying.
You may want to try to send your medic to a secluded area on the map so that he/she never gets targeted and stays alive OR the better route, you can just put your medic at the bottom of your troop list and he/she will most likely become the last person to spawn in as long as you have enough other troops to suffice the initial troop requirement for a battle. Your medic's skills will still be in effect as long as he/she is still conscious, whether on the battlefield or not. (Or at least that's what I can deduce from my personal experiences.)