The medic can heal the same person several times, BUT there are some restrictions…
Each "group" of wounds that you attempt to heal can only be healed once/24 hours.
So, if I am playing a Stormtrooper with 16 wounds, and get shot twice in the first round of combat for 4 and 5 wounds (after armor and such), and take cover behind a wall while the medic tries to heal me.. Lets say he heals me for 5 points of damage. Out of the first 2 attacks i had taken a total of 9 damage, then got healed for 5. This means I have 4 remaining wounds that are TREATED.
So if I in the few rounds of battle, or a bit later within those 24 hours, take another hit for 2 wounds (putting me at 6wounds of damage), the medic rolls and again would be able to heal 5, he would still only be able to heal those 2 later wounds, because the first 4 have already been treated.
So basically everytime you attempt a first aid, you treat ALL the wounds currently on that character. They are ALL treated, no matter how many of them you remove or not.
If I had taken 4 wounds, then gotten healed and then shot again for 5 wounds and healed, the medic would probably have been able to remove them all.
Just to clarify, and I've pulled out my OW rules now: its meaningful to note that the idea of "treated" wounds is no longer present. No matter what, you can only have one First Aid action performed on your character per day. But it can be confirmed that the Medic can perform First Aid on multiple characters.
Instead of "these wounds have been treated by the First Aid action," its just an idea that "this PC has had First Aid performed on them in the last 24 hours." Its actually possible to solely use First Aid as a means of healing a character, given enough days (i.e. you don't actually need to use extended care after the first use of the First Aid action).
This is significantly different from how it works in the previous 40k line (at leas up through DW, I haven't run a game of BC).
As far as the usefulness of medics: as others have said, they get +5 int, and cheap access to pretty much all healing related talents/skills. Ultimately it comes down to how useful you find their comrade abilities to be (because after enough XP is earned, that +5 int isn't going to be that meaningful). They can improve their ability to make use of Extended Care (and thus makes them excellent healers out of combat), and most interestingly, the ablity to have comrades perform medicae checks at range (remember, First Aid is a Full Action). This is probably the key thing, as it frees up their economy of actions and allows them to aid allies without needlessly exposing themselves to enemy fire.
Overall I'd say they're useful, but by no means "mandatory" (given the removal of the idea of treated/untreated wounds for the First Aid action, the net healing they can perform daily is limited). Fortunately the increase to make degrees of success add to the final result does by all means make medic useful, and First Aid at range has plenty of uses. What would probably determine their usefulness as well is what the GM would provide the party in their absence. Does the GM opt to provide an Advanced Medkit as a part of mission gear? How well staffed are allied medical facilities? If the GM is too lenient in the absence of a Medic, then much of the Medic's usefullness is decreased. Of course, if the GM is too harsh on the matter, then the party will needlessly suffer for the sake of the players actually picking the specialties they want.