I doubt that any available medical imaging equipment is sensitive enough to pick up an etched engraving.  In the first place, x-rays are very low resolution.  CT and MRI don't work with metal objects because of extensive scattering and noise.

When you engrave characters to metal, this changes the metal's shape, making the characters clearly readable with pretty much any sort of reflective radiation.  The tamper proof case may look great but what if tampering is unnecessary because any physician can take it to work and see through the case with medical imaging gear?  An engraved secret in a metal coin is also going to be vulnerable to magnetic imaging techniques.