While I have a special love for medical staff in the armed forces, it's really not the kind of thing that would make sense being included as a support battalion in HOI4.
HOI3 did it right with the medical techs. If you allow an actual support battalion that does this job, everyone will employ it, and then I will find the optimum ratio to employ so that all my armored divisions becomes self-healing tanks, creating an infinite loop with an MMO.
IMHO there's no point in representing medical units without proper logistics since it is the main limiting factor.
There's no point in representing medical units without some sort of non-material cost associated with them, either. Doctors don't grow on trees; for that matter, corpsmen don't grow on trees. Tons of training and expertise needed to churn out even a modest number of folks to staff such units.