No, on both questions, at least in my experience.
Most enlisted soldiers and NCOs I know realize that physicians are around for a very specific role. Fulfill that role, and don't wear your uniform backwards, and they'll leave you alone. Besides, they all know to respect the rank, not the man (woman). Everyone knows an NCO that gets a kick out of correcting a MC officer's uniform, but that's about the extent of any flak you'll get.
As far as being a "real" soldier, I'd say no as well. Then again, a lot of these enlisted folks aren't exactly kicking down doors or going out on patrols either, so how do you define someone as a real soldier? Most of the military serves in a support function, so if you think of a soldier as a trigger puller, then most of us won't qualify.