Pretty good heals early on, but somewhat relies on healing upgrades late game. I've been fine with just green meds though. I almost always use a tac14 on this build, since it doesn't need damage cards to handle tallboys or it's variants(with decent team mates). If my team is doing well enough against specials, or is just lacking in horde clear, I'll run the 870. I ignore hunker down, and get shell carrier in this case, since ammo is more of a problem, and the 870 doesn't need the accuracy. If we're not doing well against specials, I can pick up shredder at the 5th map in act 1, earlier on 2/3. Mid-late game I have enough copper to consistently max out my med kits. You could also only buy bandages, and have your team mates buy med kits that they can drop for you. But with quickplay being...well...quickplay, you shouldn't assume your team mates will always cooperate. There's enough copper in this build to supply the minimum 3 med slots with med kits every round either way.
The med kits can help people who get some serious ouchy's, while any meds on your team mates, or in game, can go to touch ups. This build requires some competence from everyone, where most people are taking small amounts of dmg most of the time. I have enough on this build where I can nearly full heal team mates with a blue medkit, and also take off 25 trauma. I barely need to full heal people unless shit hits the fan though, so grey/green med kits are usually enough. What normally happens is I heal their chip damage with bandages they have. When they have enough trauma to not waste however much trauma heal I have, I use the med kit. Only if they have red health as well though. I'm not using a med kit if they have full white health and like 20 trauma. Just wait till they inevitably take more damage.