No, but support units are often left to provided security for themselves and such. The classic example is Jessica Lynch. A support unit with men and women, in Iraq, a place where no defined areas combat are expected. That is the way combat is.
Doc's, nurse and other highly trained specialties are usually protected or outside a combat theatre, but they are also in danger at times.
Yes and that brings back my point that our military leaders were stupid for putting non-combat units within a combat zone.