Since having to use the system whilst stationed in Cyprus in the mid 90's, I can only say - if only the whole system worked as efficiently as this.
On the subject of short-cutting the system, my recollections are that not every individual posted or detached oversees was aware of it; I was given cards with the Compasionate Cell 24 hour number on them to give to my parents and in-laws. Yet when on Ord Sgt at Akrotiri I recieved a good number of late night calls from distraught relatives trying to get in touch with 'SAC Bloggs' because a family member was gravely ill and they needed Bloggs home ASAP. I made a point of ensuring I always had the Comp Cell number available when on duty NCO in case of such a call, because it wasn't always as prominently displayed in the MGR as IMHO it should have been.