Yes, the metal's shape is changed...but the imaging equipment is not nearly sensitive enough to pick up etched characters on a coin... we're talking perhaps two thousandths of an inch in depth.  Medical imaging equipment could determine the difference between a 50 cent piece and a silver dollar, because of size.  It could not differentiate between a Canadian quarter vs a US quarter, let alone etching on a coin's surface... not even close.  Furthermore, MRI and CT cannot accurately image metallic objects because of extensive noise and scattering.